ORCID Profile
0000-0002-4407-9238
Current Organisation
University of New South Wales
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Publisher: American Mathematical Society (AMS)
Date: 31-10-2009
Publisher: Cambridge University Press (CUP)
Date: 13-01-2023
DOI: 10.1017/S0004972722001617
Abstract: We prove some zero density theorems for certain families of Dirichlet L -functions. More specifically, the subjects of our interest are the collections of Dirichlet L -functions associated with characters to moduli from certain sparse sets and of certain fixed orders.
Publisher: World Scientific Pub Co Pte Ltd
Date: 27-03-2023
DOI: 10.1142/S1793042123500793
Abstract: We evaluate the smoothed first moment of central values of a family of quadratic Hecke [Formula: see text]-functions in the Gaussian field using the method of double Dirichlet series. The asymptotic formula we obtain has an error term of size [Formula: see text] under the generalized Riemann hypothesis. The same approach also allows us to obtain asymptotic formulas for all [Formula: see text], [Formula: see text] for a smoothed double character sum involving [Formula: see text], where [Formula: see text] denotes the quadratic symbol in the Gaussian field.
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2016
Publisher: Mathematical Sciences Publishers
Date: 13-09-2021
Publisher: Springer Science and Business Media LLC
Date: 14-02-2020
Publisher: Cambridge University Press (CUP)
Date: 29-10-2022
DOI: 10.1017/S1446788720000397
Abstract: In this paper, we prove a one level density result for the low-lying zeros of quadratic Hecke L -functions of imaginary quadratic number fields of class number 1. As a corollary, we deduce, essentially, that at least $(19-\\cot (1/4))/16 = 94.27\\ldots \\%$ of the L -functions under consideration do not vanish at 1/2.
Publisher: Elsevier BV
Date: 2008
Publisher: Elsevier BV
Date: 10-2008
Publisher: Elsevier BV
Date: 2023
Publisher: Springer Science and Business Media LLC
Date: 29-09-2013
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2013
DOI: 10.4064/AA158-4-3
Publisher: Springer Science and Business Media LLC
Date: 31-03-2007
Publisher: Cambridge University Press (CUP)
Date: 12-04-2012
DOI: 10.1017/S001309151100037X
Abstract: We investigate the first and second moments of shifted convolutions of the generalized isor function d 3 ( n ).
Publisher: Canadian Mathematical Society
Date: 30-08-2020
DOI: 10.4153/S0008414X1900021X
Abstract: In this paper we prove some one-level density results for the low-lying zeros of families of quadratic and quartic Hecke $L$ -functions of the Gaussian field. As corollaries, we deduce that at least 94.27% and 5%, respectively, of the members of the quadratic family and the quartic family do not vanish at the central point.
Publisher: Wiley
Date: 07-09-2011
DOI: 10.1112/S0010437X10004914
Abstract: In this paper, we prove some one level density results for the low-lying zeros of families of L -functions. More specifically, the families under consideration are that of L -functions of holomorphic Hecke eigenforms of level 1 and weight k twisted with quadratic Dirichlet characters and that of cubic and quartic Dirichlet L -functions.
Publisher: World Scientific Pub Co Pte Lt
Date: 09-2009
DOI: 10.1142/S1793042109002523
Abstract: We verify the Hardy–Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper by the authors [3].
Publisher: Oxford University Press (OUP)
Date: 14-07-2012
DOI: 10.1093/QMATH/HAR018
Publisher: Wiley
Date: 12-2005
Publisher: Elsevier BV
Date: 10-2018
Publisher: Cambridge University Press (CUP)
Date: 27-02-2019
DOI: 10.1017/S0004972719000224
Abstract: We prove a lower bound for the large sieve with square moduli.
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2019
DOI: 10.4064/AA170827-9-3
Publisher: Oxford University Press (OUP)
Date: 10-04-2016
DOI: 10.1093/IMRN/RNW013
Publisher: Springer Science and Business Media LLC
Date: 18-10-2007
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 2006
DOI: 10.4171/RMI/458
Publisher: Cambridge University Press (CUP)
Date: 22-02-2023
DOI: 10.1017/S1446788721000410
Abstract: In this paper, we study lower-order terms of the one-level density of low-lying zeros of quadratic Hecke L -functions in the Gaussian field. Assuming the generalized Riemann hypothesis, our result is valid for even test functions whose Fourier transforms are supported in $(-2, 2)$ . Moreover, we apply the ratios conjecture of L -functions to derive these lower-order terms as well. Up to the first lower-order term, we show that our results are consistent with each other when the Fourier transforms of the test functions are supported in $(-2, 2)$ .
Publisher: World Scientific Pub Co Pte Ltd
Date: 21-04-2022
DOI: 10.1142/S1793042122500877
Abstract: In this paper, we establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal [S. Baier and A. Bansal, The large sieve with power moduli for [Formula: see text], Int. J. Number Theory 14 (10) (2018) 2737–2756 Large sieve with sparse sets of moduli for [Formula: see text], Acta Arith. 196 (1) (2020) 17–34] for the Gaussian field.
Publisher: Elsevier BV
Date: 04-2020
Publisher: Springer Science and Business Media LLC
Date: 14-05-2020
Publisher: Adam Mickiewicz University (Euclid)
Date: 12-2020
DOI: 10.7169/FACM/1857
Publisher: Elsevier BV
Date: 11-2021
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2004
DOI: 10.4064/AA112-3-5
Publisher: Cellule MathDoc/CEDRAM
Date: 21-05-2021
DOI: 10.5802/JTNB.1149
Publisher: Springer Science and Business Media LLC
Date: 27-09-2023
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 2006
DOI: 10.4064/AA125-2-5
Publisher: Wiley
Date: 10-08-2019
DOI: 10.1112/MTK.12219
Abstract: We establish lower bounds for the discrete 2 k th moment of the derivative of the Riemann zeta function at nontrivial zeros for all under the Riemann hypothesis and the assumption that all zeros of are simple.
Publisher: Elsevier BV
Date: 06-2023
Publisher: Elsevier BV
Date: 11-2022
Publisher: Wiley
Date: 20-12-2010
DOI: 10.1112/JLMS/JDP064
Location: Singapore
No related grants have been discovered for Liangyi Zhao.