Si-Zhe Xie

activity

20232026

collaborators

4 papers

math.NT2026

Prime pairs along rays of prime indices

Shenghao Hua, Sizhe Xie

Let $p_{j}$ be the prime with index $j$ . We prove that the ratios $m / n$ for which $p_{m} + p_{n}$ is a square are dense in $R_{> 0}$ . The same is true when $∣ p_{m} - p_{n} ∣$ is a square.…

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.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…

math.NT2023

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 $L (\frac{1}{2}, χ_{p})$ with prime numbers $p \equiv 1 (mod 8)$ .

Prime pairs along rays of prime indices

Multiple Gauss sums

Forms in prime variables and differing degrees

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

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