Hao Zhang

activity

20232026

collaborators

Showing 2025Show all

6 papers · 1 filter

math.NT2025

Large values of quadratic character sums revisited

Zikang Dong, Ruihua Wang, Weijia Wang +1

We study large values of quadratic character sums with summation lengths exceeding the square root of the modulus. Assuming the Generalized Riemann Hypothesis, we obtain a new Omeg…

math.NT2025

Large quadratic character sums with multiplicative coefficients

Zikang Dong, Yutong Song, Weijia Wang +2

In this article, we investigate conditional large values of quadratic Dirichlet character sums with multiplicative coefficients. We prove some Omega results under the assumption of…

math.NT2025

Large values of Dirichlet polynomials with multiplicative coefficients

Zikang Dong, Yutong Song, Weijia Wang +2

In this paper, we investigate large values of Dirichlet polynomials with multiplicative coefficients $\sum_{n \leq N} f (n) n^{i t}$ , where $1 ≪ t \leq T$ for large $T$ . We prove an impro…

math.NT2025

Large character sums with multiplicative coefficients

Zikang Dong, Yutong Song, Weijia Wang +2

In this paper, we investigate large values of Dirichlet character sums with multiplicative coefficients $\sum_{n \leq N} f (n) χ (n)$ . We prove a new Omega result in the region $\exp((\l…

math.NT2025

The Diophantine Frobenius Problem revisited

Yuchen Ding, Weijia Wang, Hao Zhang

Let $k \geq 2$ and $a_{1}, a_{2}, \dots, a_{k}$ be positive integers with \[ \gcd(a_1, a_2, \cdots, a_k)=1. \] It is proved that there exists a positive integer $G_{a_1, a_2, \cdots, a_k}…

math.NT2025

Lower bounds for high moments of zeta sums

Zikang Dong, Weijia Wang, Hao Zhang

In this article, we investigate high moments of zeta sums $\sum_{n \leq x} n^{i t}$ . We show unconditional lower bounds for them.