Shengbo Zhao

collaborators

9 papers

math.NT2026

Joint extreme values of Dirichlet (L)-functions and their logarithmic derivatives

Shengbo Zhao

In this paper, we establish joint extreme values of Dirichlet (L)-functions and their logarithmic derivatives using the resonance method. Our results extend previous work of Aistle…

math.NT2025

Note on large quadratic character sums

Zikang Dong, Yutong Song, Ruihua Wang +1

In this article, we investigate the conditional large values of quadratic Dirichlet character sums. We prove an Omega result for quadratic character sums under the assumption of th…

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

Quadratic character sums with multiplicative coefficients

Zikang Dong, Zhonghua Li, Yutong Song +1

In this article, we study extreme values of quadratic character sums with multiplicative coefficients $\sum_{n \leq N} f (n) χ_{d} (n)$ . For a positive number $N$ within a suitable range,…