Select Publications

Journal articles

Gao P; Zhao L, 2024, 'Moments of Dirichlet $L$-functions to a fixed modulus over function fields', International Journal of Number Theory

Gao P; Zhao L, 2023, 'Moments and one level density of sextic Hecke L-functions', Functiones et Approximatio Commentarii Mathematici, http://dx.doi.org/10.7169/facm/2057

Gao P; Zhao L, 2023, 'Subconvexity of a double Dirichlet series over the Gaussian field', Quarterly Journal of Mathematics, 74, pp. 1237 - 1252, http://dx.doi.org/10.1093/qmath/haad023

Gao P; Zhao L, 2023, 'Ratios conjecture for quadratic Hecke L-functions in the Gaussian field', Monatshefte fur Mathematik, 203, pp. 63 - 90, http://dx.doi.org/10.1007/s00605-023-01903-5

Corrigan C; Zhao L, 2023, 'Zero-Density Theorems for Families of Dirichlet L-functions', Bulletin of the Australian Mathematical Society, 108, pp. 224 - 235, http://dx.doi.org/10.1017/S0004972722001617

Gao P; Zhao L, 2023, 'Twisted first moment of quadratic and quadratic twist $L$-functions', Functiones et Approximatio Commentarii Mathematici, http://dx.doi.org/10.7169/facm/2120

Gao P; Zhao L, 2023, 'Lower bounds for negative moments of $ζ'(ρ)$', Mathematika: a journal of pure and applied mathematics, 69, pp. 1081 - 1103, http://dx.doi.org/10.1112/mtk.12219

Gao P; Zhao L, 2023, 'First moment of central values of quadratic Hecke L-functions in the Gaussian field', International Journal of Number Theory, 19, pp. 1621 - 1637, http://dx.doi.org/10.1142/s1793042123500793

Gao P; Zhao L, 2023, 'One-level density of quadratic twists of L-functions', Acta Arithmetica, 207, pp. 201 - 215, http://dx.doi.org/10.4064/aa220613-13-12

Gao PENG; Zhao L, 2023, 'Lower-order terms of the one-level density of a family of quadratic Hecke L-functions', Journal of the Australian Mathematical Society, 114, pp. 178 - 221, http://dx.doi.org/10.1017/S1446788721000410

Gao P; Zhao L, 2023, 'Mean squares of quadratic twists of the Möbius function', Journal of Number Theory, 247, pp. 1 - 14, http://dx.doi.org/10.1016/j.jnt.2022.12.007

Gao P; Zhao L, 2023, 'First moment of central values of quadratic Hecke $L$-functions in the Gaussian field', International Journal of Number Theory, http://dx.doi.org/10.1142/S1793042123500793

Gao P; Zhao L, 2023, 'Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli', Colloquium Mathematicum, 171, pp. 61 - 77, http://dx.doi.org/10.4064/cm8650-1-2022

Gao P; Zhao L, 2023, 'Moments of quadratic Dirichlet L-functions over function fields', Finite Fields and Their Applications, 85, pp. 102113 - 102113, http://dx.doi.org/10.1016/j.ffa.2022.102113

Gao P; Zhao L, 2023, 'Mean squares of quadratic twists of the Möbius function', Journal of Number Theory, 247, pp. 1 - 14, http://dx.doi.org/10.1016/j.jnt.2022.12.007

Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet $L$-functions', Indagationes Mathematicae, 33, pp. 1263 - 1296, http://dx.doi.org/10.1016/j.indag.2022.08.003

Gao P; Zhao L, 2022, 'Average values of quadratic Hecke character sums', Journal- Ramanujan Mathematical Society, 37, pp. 99 - 107, http://arxiv.org/abs/1910.09691v2

Gao P; Zhao L, 2022, 'One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields', Journal of the Australian Mathematical Society, 112, pp. 170 - 192, http://dx.doi.org/10.1017/S1446788720000397

Gao P; Zhao L, 2022, 'Average values of quadratic Hecke character sums', Journal of the Ramanujan Mathematical Society, 37, pp. 99 - 107, http://dx.doi.org/10.48550/arXiv.1910.09691

Gao P; Zhao L, 2022, 'First Moments of Some Hecke $L$-functions of Prime Moduli', Functiones et Approximatio Commentarii Mathematici, 66, pp. 161 - 178, http://dx.doi.org/10.7169/facm/1936

Gao P; Zhao L, 2022, 'The Large Sieve with Power Moduli in Imaginary Quadratic Number Fields', International Journal of Number Theory, 18, pp. 1713 - 1733, http://dx.doi.org/10.1142/S1793042122500877

Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet L-functions', Indagationes Mathematicae, http://dx.doi.org/10.1016/j.indag.2022.08.003

Gao P; Zhao L, 2021, 'Moments and One level density of certain unitary families of Hecke {$L$}-functions', Journal de Theorie des Nombres de Bordeaux, 33, pp. 1 - 16, http://dx.doi.org/10.5802/jtnb.1149

Gao P; Zhao L, 2021, 'Value-distribution of quartic Hecke $L$-functions', Moscow Journal of Combinatorics and Number Theory, 10, pp. 167 - 181, http://dx.doi.org/10.2140/moscow.2021.10.167

Gao P; Zhao L, 2021, 'One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli', The Hardy-Ramanujan Journal, 43, pp. 173 - 187, http://arxiv.org/abs/2005.04811v1

Gao P; Zhao L, 2021, 'Moments and One level density of certain unitary families of Hecke L-functions', JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 33, pp. 1 - 16, http://dx.doi.org/10.5802/jtnb.1149

Gao P; Zhao L, 2021, 'Moments of central values of quartic Dirichlet L-functions', Journal of Number Theory, 228, pp. 342 - 358, https://www.sciencedirect.com/science/article/pii/S0022314X21001591?via%3Dihub

Gao P; Zhao L, 2020, 'Mean values of cubic and quartic Dirichlet Characters', Functiones et Approximatio Commentarii Mathematici, 63, pp. 227 - 245, http://dx.doi.org/10.7169/facm/1857

Gao P; Zhao L, 2020, 'Low-lying zeros of a family of quadratic Hecke $L$-functions via ratios conjecture', , http://arxiv.org/abs/2007.13265v2

Gao P; Zhao L, 2020, 'First Moments of Some Hecke $L$-functions of Prime Moduli', Funct. Approx. Comment. Math., Vol. 66, 2022, No. 2, pp. 161--178, http://dx.doi.org/10.7169/facm/1936

Gao P; Zhao L, 2020, 'One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions', Canadian Journal of Mathematics, 72, pp. 427 - 454

Gao P; Zhao L, 2020, 'Moments of central values of cubic Hecke $L$-functions of $\mathbb{Q}(i)$', Research in Number Theory, 6, http://dx.doi.org/10.1007/s40993-020-0189-3

Gao P; Zhao L, 2020, 'Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields', Journal of Number Theory, 209, pp. 359 - 377, http://dx.doi.org/10.1016/j.jnt.2019.09.002

Gao P; Zhao L, 2020, 'One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli', Hardy-Ramanujan Journal, 43, pp. 173 - 187, http://dx.doi.org/10.46298/hrj.2021.7461

Gao P; Zhao L, 2019, 'Lower order terms of the one level density of a family of quadratic Hecke $L$-functions', Journal of the Australian Mathematical Society

Gao P; Zhao L, 2019, 'Weighted first moments of some special quadratic Dirichlet $L$-functions', New Zealand Journal of Mathematics, 49, pp. 31 - 40, http://arxiv.org/abs/1802.03896v2

Gao P; Zhao L, 2019, 'First Moment of Hecke $L$-functions with quartic characters at the central point', Mathematische Zeitschrift, 294, pp. 1841 - 1854

Gao P; Zhao L, 2019, 'Primes $p \equiv 1 \bmod{d}$ and $a^{(p-1)/d} \equiv 1 \bmod{p}$}', Integers : Electronic Journal of Combinatorial Number Theory, 19, http://arxiv.org/abs/1807.09410v1

Baier S; Lynch S; Zhao L, 2019, 'A Lower Bound for the Large Sieve with Square Moduli', Bulletin of the Australian Mathematical Society, 100, pp. 225 - 225, http://dx.doi.org/10.1017/S0004972719000224

Gao P; Zhao L, 2019, 'PRIMES p ≡ 1 mod d AND a(p1)/d ≡ 1 mod p', Integers, 19

Gao P; Zhao L, 2019, 'WEIGHTED FIRST MOMENTS OF SOME SPECIAL QUADRATIC DIRICHLET L-FUNCTIONS', New Zealand Journal of Mathematics, 49, pp. 31 - 40

Gao P; Zhao L, 2019, 'Mean values of some Hecke characters', Acta Arithmetica, 187, pp. 125 - 141

Gao P; Zhao L, 2018, 'Mean values of divisors of forms $n^2+Nm^2$', , http://arxiv.org/abs/1812.07863v1

Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, 191, pp. 194 - 212

Gao P; Zhao L, 2017, 'Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$', Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$, http://arxiv.org/abs/1710.04909v2

Baker RC; Zhao L, 2016, 'Gaps between primes in Beatty sequences', Acta Arithmetica, 172, pp. 207 - 242, http://dx.doi.org/10.4064/aa7993-1-2016

Baker RC; Zhao L, 2016, 'Gaps of Smallest Possible Order between Primes in an Arithmetic Progression', International Mathematics Research Notices, pp. 7341 - 7368, http://dx.doi.org/10.1093/imrn/rnw013

Foo T; Zhao L, 2013, 'On primes represented by cubic polynomials', Mathematische Zeitschrift, 274, pp. 323 - 340, http://dx.doi.org/10.1007/s00209-012-1072-2

Baier S; Zhao L, 2013, 'On Hecke eigenvalues at primes of the form [g(n)]', Acta Arithmetica, 158, pp. 341 - 357, http://dx.doi.org/10.4064/aa158-4-3

Gao P; Zhao L, 2012, 'Large sieve inequalities for quartic characters', Quarterly Journal of Mathematics, 63, pp. 891 - 917, http://dx.doi.org/10.1093/qmath/har018


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