Shifan Zhao

activity

20242026

collaborators

5 papers

math.NT2026

On Ramanujan Primes for Hecke-Maass Cusp Forms

Tinghao Huang, Shifan Zhao

For a primitive Hecke-Maass cusp form $I ¨ $ of level $N$ with the $n$ -th Hecke eigenvalue $I^»_{I ¨} (n)$ and a prime number $p ∤ N$ , the celebrated Ramanujan conjecture at $p$ assert…

math.NT2026

Landau-Siegel Zeros of Triple Product L-functions

Shifan Zhao

Let $F$ be a number field. Let $I ¨ _{1}, I ¨ _{2}$ be cuspidal automorphic representations of $G L_{2} (A_{F})$ , and let $I ¨ $ be a cuspidal automorphic representation of either $GL_2(\m…

math.NT2026

Landau-Siegel zeros of Rankin-Selberg $L$ -functions

Jesse Thorner, Shifan Zhao

We establish standard zero-free regions with no exceptional Landau-Siegel zeros for Rankin-Selberg $L$ -functions and triple product $L$ -functions in several new families for which…

math.NT2025

Low-lying zeros of Hilbert modular $L$ -functions weighted by powers of central $L$ -values

Zhining Wei, Liyang Yang, Shifan Zhao

Let $F (k, q)$ be the set of primitive Hilbert modular forms of weight $k$ and prime level $q$ , with trivial central character. We s…

math.NT2024

Relative Trace Formula and Uniform non-vanishing of Central $L$ -values of Hilbert Modular Forms

Zhining Wei, Liyang Yang, Shifan Zhao

Let $F (k, q)$ be the set of normalized Hilbert newforms of weight $k$ and prime level $q$ . In this paper, utilizing regularized rel…

On Ramanujan Primes for Hecke-Maass Cusp Forms

Landau-Siegel Zeros of Triple Product L-functions

Landau-Siegel zeros of Rankin-Selberg L-functions

Low-lying zeros of Hilbert modular L-functions weighted by powers of central L-values

Relative Trace Formula and Uniform non-vanishing of Central L-values of Hilbert Modular Forms

Landau-Siegel zeros of Rankin-Selberg $L$ -functions

Low-lying zeros of Hilbert modular $L$ -functions weighted by powers of central $L$ -values

Relative Trace Formula and Uniform non-vanishing of Central $L$ -values of Hilbert Modular Forms