Select Publications

By Dr Lee Zhao

Preprints

Gao P; Zhao L, 2024, Lower bounds for shifted moments of Dirichlet $L$-functions of fixed modulus, http://arxiv.org/abs/2411.03692v1

Gao P; Zhao L, 2024, Upper bounds for shifted moments of quadratic Dirichlet $L$-functions over function fields, http://arxiv.org/abs/2408.02880v1

Gao P; Zhao L, 2024, Shifted moments of quadratic Dirichlet $L$-functions, http://arxiv.org/abs/2406.18024v1

Gao P; Zhao L, 2024, Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli, http://arxiv.org/abs/2404.05081v1

Gao P; Zhao L, 2024, Ratios conjecture of quartic $L$-functions of prime moduli, http://arxiv.org/abs/2402.17198v1

Gao P; Zhao L, 2024, Bounds for moments of quadratic Dirichlet character sums, http://dx.doi.org/10.1017/S0004972724000327

Gao P; Zhao L, 2023, Ratios conjecture of cubic $L$-functions of prime moduli, http://arxiv.org/abs/2311.08626v2

Gao P; Zhao L, 2023, Ratios conjecture for primitive quadratic Hecke $L$-functions, http://arxiv.org/abs/2309.13811v1

Gao P; Zhao L, 2023, First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters, http://dx.doi.org/10.48550/arxiv.2308.10602

Gao P; Zhao L, 2023, First moment of central values of Hecke $L$-functions with Fixed Order Characters, http://arxiv.org/abs/2306.10726v2

Gao P; Zhao L, 2023, First moment of central values of quadratic Dirichlet $L$-functions, http://arxiv.org/abs/2303.11588v4

Gao P; Zhao L, 2023, Negative first moment of quadratic twists of $L$-functions, http://arxiv.org/abs/2303.05055v2

Gao P; Zhao L, 2023, Twisted first moment of quadratic and quadratic twist $L$-functions, http://dx.doi.org/10.48550/arxiv.2301.12615

Gao P; Zhao L, 2022, Mean squares of quadratic twists of the Möbius function, http://dx.doi.org/10.48550/arxiv.2212.09241

Gao P; Zhao L, 2022, Subconvexity of a double Dirichlet series over the Gaussian field, http://dx.doi.org/10.48550/arxiv.2211.08481

Corrigan CC; Zhao L, 2022, Zero-Density Theorems for Families of Dirichlet $L$-functions, http://dx.doi.org/10.1017/S0004972722001617

Gao P; Zhao L, 2022, Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field, http://dx.doi.org/10.48550/arxiv.2210.08840

Gao P; Zhao L, 2022, Moments of quadratic Dirichlet $L$-functions over Function Fields

Gao P; Zhao L, 2022, Lower bounds for negative moments of $\zeta'(\rho)$, http://dx.doi.org/10.48550/arxiv.2208.06922

Gao P; Zhao L, 2022, First moment of central values of quadratic Hecke $L$-functions in the Gaussian field, http://dx.doi.org/10.48550/arxiv.2207.03746

Gao P; Zhao L, 2022, One-level density of quadratic twists of $L$-functions, http://dx.doi.org/10.4064/aa220613-13-12

Gao P; Zhao L, 2022, Non-vanishing of quadratic twists of modular $L$-functions of prime-related moduli, http://arxiv.org/abs/2205.01824v1

Gao P; Zhao L, 2022, Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$, http://dx.doi.org/10.48550/arxiv.2201.01885

Gao P; Zhao L, 2021, Lower bounds for moments of quadratic twists of modular $L$-functions, http://arxiv.org/abs/2110.02365v3

Gao P; Zhao L, 2021, Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli, http://dx.doi.org/10.48550/arxiv.2105.03601

Gao P; Zhao L, 2021, Bounds for moments of cubic and quartic Dirichlet $L$-functions, http://dx.doi.org/10.48550/arxiv.2104.09909

Gao P; Zhao L, 2021, Moments of central values of quartic Dirichlet $L$-functions, http://dx.doi.org/10.48550/arxiv.2102.02373

Gao P; Zhao L, 2019, Lower order terms of the one level density of a family of quadratic Hecke $L$-functions, http://dx.doi.org/10.48550/arxiv.1912.05041

Gao P; Zhao L, 2019, Mean values of cubic and quartic Dirichlet Characters, http://dx.doi.org/10.48550/arxiv.1902.10987

Baier S; Lynch SB; Zhao L, 2018, A Lower Bound for the Large Sieve with Square Moduli, http://dx.doi.org/10.48550/arxiv.1812.05844

Gao P; Zhao L, 2018, Value-distribution of quartic Hecke $L$-functions, http://dx.doi.org/10.48550/arxiv.1809.09822

Gao P; Zhao L, 2018, Moments and One level density of certain unitary families of Hecke {$L$}-functions, http://dx.doi.org/10.48550/arxiv.1808.01710

Gao P; Zhao L, 2017, One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields, http://dx.doi.org/10.48550/arxiv.1711.10557

Gao P; Zhao L, 2017, Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields, http://dx.doi.org/10.48550/arxiv.1707.00091

Gao P; Zhao L, 2017, First Moment of Hecke $L$-functions with quartic characters at the central point, http://dx.doi.org/10.48550/arxiv.1706.05450

Shparlinski IE; Zhao L, 2016, Elliptic curves in isogeny classes, http://dx.doi.org/10.48550/arxiv.1611.05258

Gao P; Zhao L, 2009, One level density of low-lying zeros of families of $L$-functions, http://dx.doi.org/10.48550/arxiv.0910.5063

Baier S; Zhao L, 2008, On Hecke Eigenvalues at Piatetski-Shapiro Primes, http://dx.doi.org/10.48550/arxiv.0808.1756

Baier S; Zhao L, 2007, On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves, http://dx.doi.org/10.48550/arxiv.0708.2987

Baier S; Zhao L, 2006, Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli, http://dx.doi.org/10.48550/arxiv.math/0602116

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