Sizhe Xie

activity

20242026

collaborators

3 papers

math.NT2026

Multiple Gauss sums

Jianya Liu, Sizhe Xie

A multiple Gauss sum is a complete multiple exponential sum twisted by Dirichlet characters. We prove a new bound for multiple Gauss sums and, as an application, improve previous r…

math.NT2025

Extreme central values of quadratic Dirichlet $L$ -functions with prime conductors

Mingyue Fan, Shenghao Hua, Sizhe Xie

In this paper we prove a lower bound result for extremely large values of $L (\frac{1}{2}, I ¨ _{p})$ with prime numbers $p \equiv 1 (mod 8)$ .

math.NT2024

Forms in prime variables and differing degrees

Jianya Liu, Sizhe Xie

Let $F_{1}, \dots, F_{R}$ be homogeneous polynomials with integer coefficients in $n$ variables with differing degrees. Write $F = (F_{1}, \dots, F_{R})$ with $D$ being the maxima…

Multiple Gauss sums

Extreme central values of quadratic Dirichlet L-functions with prime conductors

Forms in prime variables and differing degrees

Extreme central values of quadratic Dirichlet $L$ -functions with prime conductors