By Associate Professor Lee Zhao

Preprints

Gao P; Zhao L, 2026, Large values of cubic and quartic Dirichlet $L$-functions of prime moduli, https://arxiv.org/abs/2609.02392v1

Gao P; Zhao L, 2026, Murmurations of quadratic Hecke $L$-functions of the Gaussian field, https://arxiv.org/abs/2607.20853v1

Gao P; Zhao L, 2026, High moments of random multiplicative functions twisted by Fourier coefficients of modular forms, https://arxiv.org/abs/2606.01514v1

Gao P; Zhao L, 2026, Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms, https://arxiv.org/abs/2604.09968v1

Gao P; Zhao L, 2026, First Moment of Quadratic Hecke $L$-Functions with Lower Order Term, http://dx.doi.org/10.48550/arxiv.2512.22509

Gao P; Zhao L, 2026, Shifted moments of modular $L$-functions to a fixed level, https://arxiv.org/abs/2602.01409v2

Gao P; Zhao L, 2025, Lower Bounds on High Moments of Twisted Fourier coefficients of Modular Forms, https://arxiv.org/abs/2511.02344v1

Gao P; Wu X; Zhao L, 2025, The mollified fourth moment of Dirichlet $L$-functions, https://arxiv.org/abs/2509.24690v2

Gao P; Zhao L, 2025, Shifted moments of cubic and quartic Dirichlet $L$-functions, https://arxiv.org/abs/2508.14534v2

Gao P; Zhao L, 2025, Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus, https://arxiv.org/abs/2507.18186v1

Gao P; Zhao L, 2025, Ratios conjecture of cubic $L$-functions of prime moduli, http://dx.doi.org/10.48550/arxiv.2311.08626

Gao P; Zhao L, 2025, Upper bounds for moments of Dirichlet $L$-functions to a fixed modulus, https://arxiv.org/abs/2504.17905v2

Gao P; Zhao L, 2025, Upper bounds for shifted moments of quadratic Dirichlet $L$-functions over function fields

Gao P; Zhao L, 2025, Twisted second moment of modular $L$-functions to a fixed modulus, https://arxiv.org/abs/2504.02225v1

Gao P; Zhao L, 2025, Shifted moments of quadratic Dirichlet $L$-functions

Gao P; Zhao L, 2024, Bounds for Moments of Twisted Fourier coefficients of Modular Forms, https://arxiv.org/abs/2412.12515v1

Gao P; Zhao L, 2024, Lower bounds for shifted moments of Dirichlet $L$-functions of fixed modulus, https://arxiv.org/abs/2411.03692v2

Gao P; Zhao L, 2024, Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions, http://dx.doi.org/10.48550/arxiv.2405.15980

Gao P; Zhao L, 2024, Negative first moment of quadratic twists of $L$-functions, http://dx.doi.org/10.48550/arxiv.2303.05055

Gao P; Zhao L, 2024, Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions, https://doi.org/10.4064/aa240617-6-11

Gao P; Zhao L, 2024, Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli, https://arxiv.org/abs/2404.05081v2

Gao P; Zhao L, 2024, Bounds for moments of quadratic Dirichlet character sums, http://dx.doi.org/10.48550/arxiv.2403.14634

Gao P; Zhao L, 2024, Lower bounds for moments of quadratic twists of modular $L$-functions, http://dx.doi.org/10.48550/arxiv.2110.02365

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

Gao P; Zhao L, 2023, Ratios conjecture of cubic $L$-functions of prime moduli, https://doi.org/10.1016/j.indag.2025.07.001

Gao P; Zhao L, 2023, Moments of Dirichlet $L$-functions to a fixed modulus over function fields, http://dx.doi.org/10.48550/arxiv.2203.14458

Gao P; Zhao L, 2023, Ratios conjecture for primitive quadratic Hecke $L$-functions, https://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, https://arxiv.org/abs/2306.10726v3

Gao P; Zhao L, 2023, Ratios conjecture for quadratic twist of modular $L$-functions, http://dx.doi.org/10.48550/arxiv.2304.14600

Gao P; Zhao L, 2023, Subconvexity of a double Dirichlet series over the Gaussian field, http://dx.doi.org/10.48550/arxiv.2211.08481

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

Gao P; Zhao L, 2023, Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field, http://dx.doi.org/10.48550/arxiv.2210.08840

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, One-level density of quadratic twists of $L$-functions, http://dx.doi.org/10.48550/arxiv.2206.02302

Corrigan CC; Zhao L, 2022, Zero-Density Theorems for Families of Dirichlet $L$-functions, http://dx.doi.org/10.48550/arxiv.2211.00260

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, Moments of quadratic Dirichlet $L$-functions over Function Fields, http://arxiv.org/abs/2202.07814v3

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

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

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

Gao P; Zhao L, 2022, Bounds for moments of cubic and quartic Dirichlet $L$-functions, http://dx.doi.org/10.48550/arxiv.2104.09909

Gao P; Zhao L, 2022, 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, Value-distribution of quartic Hecke $L$-functions, http://dx.doi.org/10.48550/arxiv.1809.09822

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, 2021, The Large Sieve with Power Moduli in Imaginary Quadratic Number Fields, https://arxiv.org/abs/2101.00811v2

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

Gao P; Zhao L, 2020, 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, 2020, One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli, https://arxiv.org/abs/2005.04811v2

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