ORCID Profile
0000-0001-9551-2903
Current Organisation
Radboud Universiteit Nijmegen
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Pure Mathematics | Algebra and Number Theory | Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory | Pure Mathematics not elsewhere classified | Numerical and Computational Mathematics not elsewhere classified
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Mathematical Sciences | Expanding Knowledge in the Physical Sciences |
Related Links
Publications
NEW REPRESENTATIONS FOR APÉRY-LIKE SEQUENCES
Publisher: Wiley
Date: 10-12-2009
On the irrationality measure for a $ q$-analogue of $ \zeta(2)$
Publisher: Steklov Mathematical Institute
Date: 31-08-2002
Zeta stars
Publisher: International Press of Boston
Date: 2008
A q-rious positivity
Publisher: Springer Science and Business Media LLC
Date: 30-10-2010
Diophantine properties of numbers related to Catalan's constant
Publisher: Springer Science and Business Media LLC
Date: 08-2003
On the measure of linear and algebraic independence for values of entire hypergeometric functions
Publisher: Springer Science and Business Media LLC
Date: 02-1997
DOI: 10.1007/BF02355735
A Common q-Analogue of Two Supercongruences
Publisher: Springer Science and Business Media LLC
Date: 09-03-2020
DOI: 10.1007/S00025-020-1168-7
Abstract: We give a q -congruence whose specializations $$q=-1$$ q = - 1 and $$q=1$$ q = 1 correspond to supercongruences (B.2) and (H.2) on Van Hamme’s list (in: p -Adic Functional Analysis (Nijmegen, 1996), Lecture Notes in Pure and Applied Mathematics, vol 192. Dekker, New York, pp 223–236, 1997): $$\\begin{aligned}& \\sum _{k=0}^{(p-1)/2}(-1)^k(4k+1)A_k\\equiv p(-1)^{(p-1)/2}\\ ({\\text {mod}}p^3) \\quad \\text {and}\\quad \\\\& \\sum _{k=0}^{(p-1)/2}A_k\\equiv a(p)\\ ({\\text {mod}}p^2), \\end{aligned}$$ ∑ k = 0 ( p - 1 ) / 2 ( - 1 ) k ( 4 k + 1 ) A k ≡ p ( - 1 ) ( p - 1 ) / 2 ( mod p 3 ) and ∑ k = 0 ( p - 1 ) / 2 A k ≡ a ( p ) ( mod p 2 ) , where $$p $$ p 2 is prime, $$\\begin{aligned} A_k=\\prod _{j=0}^{k-1}\\biggl (\\frac{1/2+j}{1+j}\\biggr )^3=\\frac{1}{2^{6k}}{\\left( {\\begin{array}{c}2k\\\\ k\\end{array}}\\right) }^3 \\quad \\text {for}\\ k=0,1,2,\\ldots , \\end{aligned}$$ A k = ∏ j = 0 k - 1 ( 1 / 2 + j 1 + j ) 3 = 1 2 6 k 2 k k 3 for k = 0 , 1 , 2 , … , and a ( p ) is the p th coefficient of the modular form $$q\\prod _{j=1}^\\infty (1-q^{4j})^6$$ q ∏ j = 1 ∞ ( 1 - q 4 j ) 6 (of weight 3). We complement our result with a general common q -congruence for related hypergeometric sums.
Ramanujan-type formulae and irrationality measures of some multiples of $ {\pi}$
Publisher: Steklov Mathematical Institute
Date: 31-08-2005
A study of elliptic gamma function and allies
Publisher: Springer Science and Business Media LLC
Date: 28-09-2018
Generating functions of Legendre polynomials: A tribute to Fred Brafman
Publisher: Elsevier BV
Date: 04-2012
Об оценках снизу многочленов от значений некоторых целых функций
Publisher: Steklov Mathematical Institute
Date: 1996
DOI: 10.4213/SM178
On the non-quadraticity of values of the q-exponential function and related q-series
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2009
DOI: 10.4064/AA136-3-4
On the irrationality measure of $ \pi^2$
Publisher: Steklov Mathematical Institute
Date: 31-12-2013
Logarithmic and Complex Constant Term Identities
Publisher: Springer New York
Date: 2013
The Hypergeometric Equation and Ramanujan Functions
Publisher: Springer Science and Business Media LLC
Date: 12-2003
О мере иррациональности $\pi^2$
Publisher: Steklov Mathematical Institute
Date: 2013
DOI: 10.4213/RM9564
Euler's factorial series and global relations
Publisher: Elsevier BV
Date: 05-2018
Одно из восьми чисел $\zeta(5),\zeta(7),…,\zeta(17),\zeta(19)$ иррационально
Publisher: Steklov Mathematical Institute
Date: 2001
DOI: 10.4213/MZM759
“Divergent” Ramanujan-type supercongruences
Publisher: American Mathematical Society (AMS)
Date: 03-2012
Lymphomagenic properties of a HIV p17 variant derived from a splenic marginal zone lymphoma occurred in a HIV‐infected patient
Publisher: Wiley
Date: 06-11-2018
DOI: 10.1002/HON.2562
Abstract: Despite antiretroviral therapy, HIV+ in iduals still have increased risk to develop lymphomas, including marginal zone lymphomas, suggesting that factors other than HIV-related immunosuppression are probably acting as lymphomagenic factors in the HIV setting. The possible pathogenic involvement of HIV p17 protein variants was investigated in a particularly informative case of HIV-related splenic marginal zone lymphoma, which was negative for oncogenic virus infections, thus allowing us to assess the possible direct contribution of these HIV-encoded proteins to lymphomagenesis. The presence of p17 protein was analyzed by immunohistochemistry in lymphoma tissue. Recombinant p17 protein derived from the dominant sequence detected in plasma and lymphoma biopsy was characterized for B-cell proliferation, clonogenicity in soft agar, in vitro tube formation and wound healing. Intracellular signaling was investigated by immunoblotting. HIV p17 protein was detected in reactive lymphoid follicles but not within lymphoma cells. An identical dominant variant p17 sequence, p17-Lyrm, carrying a 117 to 118 Ala-Ala insertion was detected in both plasma and lymphoma tissue. Recombinant p17-Lyrm enhanced B-cell proliferation and clonogenicity promoted the formation of capillary-like structures and enhanced endothelial cell migration. Unlike reference p17, the p17-Lyrm variant enhanced the activation of Akt and ERK, critical kinases in lymphomagenesis. p17-Lyrm clonogenic activity was dependent on the activation of Akt but not of ERK1/2. These results indicated that HIV p17 variants with distinct molecular signatures and functional properties may accumulate in lymphoid tissues of HIV-infected in iduals where they may act as a local stimulus promoting the development of lymphomas.
A supercongruence motivated by the Legendre family of elliptic curves
Publisher: Pleiades Publishing Ltd
Date: 10-2010
Legendre polynomials and Ramanujan-type series for 1/π
Publisher: Springer Science and Business Media LLC
Date: 29-06-2012
FromL-series of elliptic curves to Mahler measures
Publisher: Wiley
Date: 23-01-2012
DOI: 10.1112/S0010437X11007342
Abstract: We prove the conjectural relations between Mahler measures and L -values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for L -values of elliptic curves of conductors 27 and 36. Furthermore, we prove a new functional equation for the Mahler measure of the polynomial family (1+ X ) (1+ Y )( X + Y )− αXY , α ∈ℝ.
Experimental mathematics and mathematical physics
Publisher: American Mathematical Society
Date: 2010
Arithmetic hypergeometric series
Publisher: Steklov Mathematical Institute
Date: 30-04-2011
A hypergeometric problem
Publisher: Elsevier BV
Date: 12-2009
SOME HYPERGEOMETRIC INTEGRALS FOR LINEAR FORMS IN ZETA VALUES
Publisher: Cambridge University Press (CUP)
Date: 19-07-2018
DOI: 10.1017/S0004972718000503
Abstract: We prove new integral representations of the approximation forms in zeta values.
HYPERGEOMETRIC MODULAR EQUATIONS
Publisher: Cambridge University Press (CUP)
Date: 27-12-2018
DOI: 10.1017/S144678871800037X
Abstract: We record $\\binom{42}{2}+\\binom{23}{2}+\\binom{13}{2}=1192$ functional identities that, apart from being amazingly amusing in themselves, find application in the derivation of Ramanujan-type formulas for $1/\\unicode[STIX]{x1D70B}$ and in the computation of mathematical constants.
On a q-deformation of modular forms
Publisher: Elsevier BV
Date: 07-2019
Baker-Type Estimates for Linear Forms in the Values of $q$-Series
Publisher: Canadian Mathematical Society
Date: 16-07-0003
Abstract: We obtain lower estimates for the absolute values of linear forms of the values of generalized Heine series at non-zero points of an imaginary quadratic field II, in particular of the values of q -exponential function. These estimates depend on the in idual coefficients, not only on the maximum of their absolute values. The proof uses a variant of classical Siegel's method applied to a system of functional Poincaré-type equations and the connection between the solutions of these functional equations and the generalized Heine series.
Algebraic Independence of Mahler Functions via Radial Asymptotics
Publisher: Oxford University Press (OUP)
Date: 19-05-2015
DOI: 10.1093/IMRN/RNV139
HEDGEHOGS IN LEHMER’S PROBLEM
Publisher: Cambridge University Press (CUP)
Date: 07-09-2021
DOI: 10.1017/S0004972721000654
Abstract: Motivated by a famous question of Lehmer about the Mahler measure, we study and solve its analytic analogue.
Lost in Translation
Publisher: Springer Berlin Heidelberg
Date: 2013
Больше формул рамануджанова типа для $1/\pi^2$
Publisher: Steklov Mathematical Institute
Date: 2007
DOI: 10.4213/RM6920
Одно из чисел $\zeta(5), \zeta(7), \zeta(9), \zeta(11)$ иррационально
Publisher: Steklov Mathematical Institute
Date: 2001
DOI: 10.4213/RM427
О суперсравнении, мотивированном лежандровым семейством эллиптических кривых
Publisher: Steklov Mathematical Institute
Date: 2010
DOI: 10.4213/MZM8851
О функциональной трансцендентности $q$-дзета-значений
Publisher: Steklov Mathematical Institute
Date: 2003
DOI: 10.4213/MZM629
Hypergeometric transformations of linear forms in one logarithm
Publisher: Adam Mickiewicz University (Euclid)
Date: 12-2008
Совершенно уравновешенные гипергеометрические ряды и кратные интегралы
Publisher: Steklov Mathematical Institute
Date: 2002
DOI: 10.4213/RM542
Об иррациональности значений дзета-функции в нечетных точках
Publisher: Steklov Mathematical Institute
Date: 2001
DOI: 10.4213/RM389
An elementary proof of the irrationality of Tschakaloff series
Publisher: Springer Science and Business Media LLC
Date: 10-2007
A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS
Publisher: Cambridge University Press (CUP)
Date: 22-03-2013
DOI: 10.1017/S0004972713000233
Abstract: We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Cooper. By using this modular parametrisation we resolve a subfamily of identities involving $1/ \\pi $ which was experimentally observed by Sun.
Квадратичные преобразования и формулы Гиллеры для $1/\pi^2$
Publisher: Steklov Mathematical Institute
Date: 2007
DOI: 10.4213/MZM3676
Recurrent sequences and the measure of irrationality of values of elliptic integrals
Publisher: Springer Science and Business Media LLC
Date: 05-1997
DOI: 10.1007/BF02355088
Binomial Sums Related to Rational Approximations to z(4)
Publisher: Springer Science and Business Media LLC
Date: 03-2004
Об иррациональности значений дзета-функции Римана
Publisher: Steklov Mathematical Institute
Date: 2002
DOI: 10.4213/IM387
Two hypergeometric tales and a new irrationality measure of $$\zeta (2)$$ ζ ( 2 )
Publisher: Springer Science and Business Media LLC
Date: 06-2014
Automatic discovery of irrationality proofs and irrationality measures
Publisher: World Scientific Pub Co Pte Lt
Date: 23-10-2020
DOI: 10.1142/S1793042120400230
Abstract: We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but sometimes there is still need for a human touch.
Number Theory and Related Fields
Publisher: Springer New York
Date: 2013
О линейной независимости значений рядов Чакалова
Publisher: Steklov Mathematical Institute
Date: 2007
DOI: 10.4213/RM6119
Об обратном преобразовании Лежандра одного семейства последовательностей
Publisher: Steklov Mathematical Institute
Date: 2004
DOI: 10.4213/MZM573
Well-poised generation of Apéry-like recursions
Publisher: Elsevier BV
Date: 06-2005
Well-poised hypergeometric service for diophantine problems of zeta values
Publisher: Cellule MathDoc/CEDRAM
Date: 2003
DOI: 10.5802/JTNB.415
On the Mahler measure of hyperelliptic families
Publisher: Springer Science and Business Media LLC
Date: 14-07-2016
Generalizations of Clausen's Formula and algebraic transformations of Calabi–Yau differential equations
Publisher: Cambridge University Press (CUP)
Date: 30-03-2011
DOI: 10.1017/S0013091509000959
Abstract: We provide certain unusual generalizations of Clausen's and Orr's theorems for solutions of fourth-order and fifth-order generalized hypergeometric equations. As an application, we present several ex les of algebraic transformations of Calabi–Yau differential equations.
Approximations to q-logarithms and q-dilogarithms, with applications to q-zeta values
Publisher: Springer Science and Business Media LLC
Date: 08-2006
Irrationality of certain numbers that contain values of the di- and trilogarithm
Publisher: Springer Science and Business Media LLC
Date: 02-03-2006
Cancellation of factorials
Publisher: Steklov Mathematical Institute
Date: 31-08-2001
Сокращение факториалов
Publisher: Steklov Mathematical Institute
Date: 2001
DOI: 10.4213/SM588
On theorems of Gelfond and Selberg concerning integral-valued entire functions
Publisher: Elsevier BV
Date: 10-2004
WELL-POISED HYPERGEOMETRIC TRANSFORMATIONS OF EULER-TYPE MULTIPLE INTEGRALS
Publisher: Wiley
Date: 23-07-2004
Densities of Short Uniform Random Walks
Publisher: Canadian Mathematical Society
Date: 10-2012
Abstract: We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and, less completely, those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.
Remarks on irrationality of q-harmonic series
Publisher: Springer Science and Business Media LLC
Date: 04-2002
Very well-poised hypergeometric series and multiple integrals
Publisher: Steklov Mathematical Institute
Date: 31-08-2002
More Ramanujan-type formulae for $ 1/\pi^2$
Publisher: Steklov Mathematical Institute
Date: 30-06-2007
On the irrationality of the values of the zeta function at odd integer points
Publisher: Steklov Mathematical Institute
Date: 30-04-2001
Arithmetic of linear forms involving odd zeta values
Publisher: Cellule MathDoc/CEDRAM
Date: 2004
DOI: 10.5802/JTNB.447
Linear independence of values of Tschakaloff functions with different parameters
Publisher: Elsevier BV
Date: 09-2008
Generating functions of Legendre polynomials: A tribute to Fred Brafman
Publisher: Elsevier BV
Date: 06-2013
MAGNETIC (QUASI-)MODULAR FORMS
Publisher: Cambridge University Press (CUP)
Date: 30-05-2022
DOI: 10.1017/NMJ.2022.11
Abstract: A (folklore?) conjecture states that no holomorphic modular form $F(\\tau )=\\sum _{n=1}^{\\infty } a_nq^n\\in q\\mathbb Z[[q]]$ exists, where $q=e^{2\\pi i\\tau }$ , such that its anti-derivative $\\sum _{n=1}^{\\infty } a_nq^n/n$ has integral coefficients in the q -expansion. A recent observation of Broadhurst and Zudilin, rigorously accomplished by Li and Neururer, led to ex les of meromorphic modular forms possessing the integrality property. In this note, we investigate the arithmetic phenomenon from a systematic perspective and discuss related transcendental extensions of the differentially closed ring of quasi-modular forms.
Рекуррентные последовательности и мера иррациональности значений эллиптических интегралов
Publisher: Steklov Mathematical Institute
Date: 1997
DOI: 10.4213/MZM1560
New analogues of Clausenʼs identities arising from the theory of modular forms
Publisher: Elsevier BV
Date: 10-2011
Euler’s constant, q-logarithms, and formulas of Ramanujan and Gosper
Publisher: Springer Science and Business Media LLC
Date: 10-2006
On the transcendence degree of the differential field generated by Siegel modular forms
Publisher: Walter de Gruyter GmbH
Date: 13-01-2003
Positivity of rational functions and their diagonals
Publisher: Elsevier BV
Date: 07-2015
A refinement of Nesterenko’s linear independence criterion with applications to zeta values
Publisher: Springer Science and Business Media LLC
Date: 02-12-2009
Dedekind's -function and Rogers-Ramanujan identities
Publisher: Wiley
Date: 02-2012
DOI: 10.1112/BLMS/BDR019
Тэта-константы и дифференциальные уравнения
Publisher: Steklov Mathematical Institute
Date: 2000
DOI: 10.4213/SM530
APÉRY LIMITS FOR ELLIPTIC -VALUES
Publisher: Cambridge University Press (CUP)
Date: 19-01-2022
DOI: 10.1017/S0004972721001295
Abstract: For an (irreducible) recurrence equation with coefficients from $\\mathbb Z[n]$ and its two linearly independent rational solutions $u_n,v_n$ , the limit of $u_n/v_n$ as $n\\to \\infty $ , when it exists, is called the Apéry limit. We give a construction that realises certain quotients of L -values of elliptic curves as Apéry limits.
On simultaneous diophantine approximations to ζ ( 2
Publisher: Elsevier BV
Date: 12-2014
О биномиальных суммах, связанных с рациональными приближениями к $\zeta(4)$
Publisher: Steklov Mathematical Institute
Date: 2004
DOI: 10.4213/MZM555
Rational Approximations to A q-Analogue of π and Some Other q-Series
Publisher: Springer Vienna
Date: 2008
Two Definite Integrals That Are Definitely (and Surprisingly!) Equal
Publisher: Springer Science and Business Media LLC
Date: 31-03-2020
Regulator of modular units and Mahler measures
Publisher: Cambridge University Press (CUP)
Date: 02-01-2014
DOI: 10.1017/S0305004113000765
Abstract: We present a proof of the formula, due to Mellit and Brunault, which evaluates an integral of the regulator of two modular units to the value of the L -series of a modular form of weight 2 at s =2. Applications of the formula to computing Mahler measures are discussed.
О рекурсии третьего порядка типа Апери для $\zeta(5)$
Publisher: Steklov Mathematical Institute
Date: 2002
DOI: 10.4213/MZM673
The Inverse Legendre Transform of a Certain Family of Sequences
Publisher: Springer Science and Business Media LLC
Date: 07-2004
О мере иррациональности значений $G$-функций
Publisher: Steklov Mathematical Institute
Date: 1996
DOI: 10.4213/IM63
О диофантовых задачах для $q$-дзета-значений
Publisher: Steklov Mathematical Institute
Date: 2002
DOI: 10.4213/MZM674
Period(d)ness of L-Values
Publisher: Springer New York
Date: 2013
On the irrationality of ζ q (2)
Publisher: Steklov Mathematical Institute
Date: 31-12-2001
SÉRIES HYPERGÉOMÉTRIQUES BASIQUES, $q$-ANALOGUES DES VALEURS DE LA FONCTION ZÊTA ET SÉRIES D’EISENSTEIN
Publisher: Cambridge University Press (CUP)
Date: 28-04-2005
On rational approximations of values of a certain class of entire functions
Publisher: Steklov Mathematical Institute
Date: 30-04-1995
Experimental Mathematics and Mathematical Physics
Publisher: Office of Scientific and Technical Information (OSTI)
Date: 26-06-2009
DOI: 10.2172/964375
GHOSTS AND CONGRUENCES FOR -APPROXIMATIONS OF HYPERGEOMETRIC PERIODS
Publisher: Cambridge University Press (CUP)
Date: 02-08-2023
DOI: 10.1017/S1446788723000083
Abstract: We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and p -adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of hypergeometric and Knizhnik–Zamolodchikov (KZ) equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application, we show that the simplest ex le of a p -adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of its monodromy representation.
Формулы рамануджанова типа и меры иррациональности некоторых кратных числа $\pi$
Publisher: Steklov Mathematical Institute
Date: 2005
DOI: 10.4213/SM1376
On the algebraic structure of functional matrices of special form
Publisher: Springer Science and Business Media LLC
Date: 12-1996
DOI: 10.1007/BF02305156
Irregular continued fractions
Publisher: Cambridge University Press
Date: 03-07-2014
Identifying causal patterns and errors in adverse clinical incidents
Publisher: Taylor & Francis
Date: 21-03-2013
DOI: 10.1201/B13826-60
Appendix A Selected continued fractions
Publisher: Cambridge University Press
Date: 03-07-2014
References
Publisher: Cambridge University Press
Date: 03-07-2014
Linear independence of dilogarithmic values
Publisher: Walter de Gruyter GmbH
Date: 02-07-2015
Abstract: We establish the linear independence over ℚ \\mathbb{Q} , in both qualitative and quantitative forms, of the four numbers 1, Li 1 ( 1 / z ) = - log ( 1 - 1 / z ) \\operatorname{Li}_{1}(1/z)=-\\log(1-1/z) , Li 2 ( 1 / z ) \\operatorname{Li}_{2}(1/z) and Li 2 ( 1 / ( 1 - z ) ) \\operatorname{Li}_{2}(1/(1-z)) , for all integers z ≥ 9 z\\geq 9 or z ≤ - 8 z\\leq-8 and for rationals z = s / r z=s/r or z = 1 - s / r z=1-s/r with 1 r s 1 r s , where s is large in comparison with r .
On the Mahler Measure of 1+X+1/X+Y +1/Y
Publisher: Oxford University Press (OUP)
Date: 16-01-2013
DOI: 10.1093/IMRN/RNS285
Quadratic irrationals through a magnifier
Publisher: Cambridge University Press
Date: 03-07-2014
Hyperelliptic curves and Somos sequences
Publisher: Cambridge University Press
Date: 03-07-2014
Ramanujan-type formulae for 1/π: q-analogues
Publisher: Informa UK Limited
Date: 23-04-2018
From folding to Fibonacci
Publisher: Cambridge University Press
Date: 03-07-2014
Irrationality of values of the Riemann zeta function
Publisher: Steklov Mathematical Institute
Date: 30-06-2002
The integer part of qα + β
Publisher: Cambridge University Press
Date: 03-07-2014
Heine's basic transform and a permutation group for q-harmonic series
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2004
DOI: 10.4064/AA111-2-4
A VARIATION ON THE THEME OF NICOMACHUS
Publisher: Cambridge University Press (CUP)
Date: 28-03-2018
DOI: 10.1017/S0004972717001411
Abstract: In this paper, we prove some conjectures of K. Stolarsky concerning the first and third moments of the Beatty sequences with the golden section and its square.
The Erdős–Moser equation
Publisher: Cambridge University Press
Date: 03-07-2014
A new lower bound for {\Vert (3/2)^k\Vert }
Publisher: Cellule MathDoc/CEDRAM
Date: 2007
DOI: 10.5802/JTNB.588
Об иррациональности $\zeta_q(2)$
Publisher: Steklov Mathematical Institute
Date: 2001
DOI: 10.4213/RM460
Производные зигелевых модулярных форм и показательные функции
Publisher: Steklov Mathematical Institute
Date: 2001
DOI: 10.4213/IM345
Special Hypergeometric Motives and Their L-Functions: Asai Recognition
Publisher: Informa UK Limited
Date: 21-05-2020
On three theorems of Folsom, Ono and Rhoades
Publisher: American Mathematical Society (AMS)
Date: 04-11-2014
Hankel Determinants of Zeta Values
Publisher: SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Date: 17-12-2015
One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational
Publisher: Steklov Mathematical Institute
Date: 31-08-2001
A MAGNETIC DOUBLE INTEGRAL
Publisher: Cambridge University Press (CUP)
Date: 18-02-2019
DOI: 10.1017/S1446788718000186
Abstract: In a recent study of how the output voltage of a Hall plate is affected by the shape of the plate and the size of its contacts, U. Ausserlechner has come up with a remarkable double integral that can be viewed as a generalisation of the classical elliptic ‘arithmetic–geometric mean (AGM)’ integral. Here we discuss transformation properties of the integral, which were experimentally observed by Ausserlechner, as well as its analytical and arithmetic features including connections with modular forms.
The Erdős–Moser equation $1^{k}+2^{k}+\dots+(m-1)^{k}=m^{k}$ revisited using continued fractions
Publisher: American Mathematical Society (AMS)
Date: 05-2011
Ramanujan-type supercongruences
Publisher: Elsevier BV
Date: 08-2009
Dwork-type supercongruences through a creative q-microscope
Publisher: Elsevier BV
Date: 02-2021
On a measure of irrationality for values of $ G$-functions
Publisher: Steklov Mathematical Institute
Date: 28-02-1996
Thetanulls and differential equations
Publisher: Steklov Mathematical Institute
Date: 31-12-2000
Further explorations of Boyd's conjectures and a conductor 21 elliptic curve
Publisher: Wiley
Date: 29-01-2016
DOI: 10.1112/JLMS/JDV073
Approximations to -, di- and tri-logarithms
Publisher: Elsevier BV
Date: 05-2007
Preface
Publisher: Cambridge University Press
Date: 03-07-2014
Some preliminaries from number theory
Publisher: Cambridge University Press
Date: 03-07-2014
О мере иррациональности $q$-аналога $\zeta(2)$
Publisher: Steklov Mathematical Institute
Date: 2002
DOI: 10.4213/SM674
Derivatives of Siegel modular forms and exponential functions
Publisher: Steklov Mathematical Institute
Date: 31-08-2001
Continued fractions
Publisher: Cambridge University Press
Date: 03-07-2014
Linear independence of values of Tschakaloff series
Publisher: Steklov Mathematical Institute
Date: 28-02-2007
Metric theory of continued fractions
Publisher: Cambridge University Press
Date: 03-07-2014
О целочисленности степенных разложений, связанных с гипергеометрическими рядами
Publisher: Steklov Mathematical Institute
Date: 2002
DOI: 10.4213/MZM375
Алгебраические соотношения для кратных дзета-значений
Publisher: Steklov Mathematical Institute
Date: 2003
DOI: 10.4213/RM592
Neverending Fractions
Publisher: Cambridge University Press
Date: 03-07-2009
Abstract: Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature subject. Beginning with a standard introduction to continued fractions, the book covers a erse range of topics, from elementary and metric properties, to quadratic irrationals, to more exotic topics such as folded continued fractions and Somos sequences. Along the way, the authors reveal some amazing applications of the theory to seemingly unrelated problems in number theory. Previously scattered throughout the literature, these applications are brought together in this volume for the first time. A wide variety of exercises guide readers through the material, which will be especially helpful to readers using the book for self-study, and the authors also provide many pointers to the literature.
Lower bounds for polynomials in the values of certain entire functions
Publisher: Steklov Mathematical Institute
Date: 31-12-1996
Арифметические гипергеометрические ряды
Publisher: Steklov Mathematical Institute
Date: 2011
DOI: 10.4213/RM9420
Algebraic relations for multiple zeta values
Publisher: Steklov Mathematical Institute
Date: 28-02-2003
Complex series for 1/π
Publisher: Springer Science and Business Media LLC
Date: 14-06-2012
New irrationality measures for $q$-logarithms
Publisher: American Mathematical Society (AMS)
Date: 20-12-2005
DOI: 10.1090/S0025-5718-05-01812-0
Abstract: The three main methods used in diophantine analysis of q q -series are combined to obtain new upper bounds for irrationality measures of the values of the q q -logarithm function \[ ln q ( 1 − z ) = ∑ ν = 1 ∞ z ν q ν 1 − q ν , | z | ⩽ 1 , \ln _{q}(1-z)=\sum _{\nu =1}^{\infty }\frac {z^{\nu }q^{\nu }}{1-q^{\nu }}, \qquad |z|\leqslant 1, \] when p = 1 / q ∈ Z ∖ { 0 , ± 1 } p=1/q\in \mathbb {Z}\setminus \{0,\pm 1\} and z ∈ Q z\in \mathbb {Q} .
The new gay loneliness?: Desire and urban gay male cultures
Publisher: Routledge
Date: 28-09-2017
On the (K.2) supercongruence of Van Hamme
Publisher: Elsevier BV
Date: 2016
Quadratic transformations and Guillera’s formulas for 1/π2
Publisher: Pleiades Publishing Ltd
Date: 04-2007
О мере линейной и алгебраической независимости значений целых гипергеометрических функций
Publisher: Steklov Mathematical Institute
Date: 1997
DOI: 10.4213/MZM1503
Об алгебраической структуре функциональных матриц специального вида
Publisher: Steklov Mathematical Institute
Date: 1996
DOI: 10.4213/MZM1903
On 𝑆𝑝₄ modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds
Publisher: American Mathematical Society
Date: 2010
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End Date: 04-2017
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