Zikang Dong

collaborators

16 papers

math.NT2026

Extreme values of Dirichlet $L$ -functions on the critical line with a growing prime modulus

Zikang Dong, Qiyu Yang, Shengbo Zhao

In this paper, we obtain extreme values of Dirichlet $L$ -functions on the critical line with a growing prime modulus. Our result yields a larger lower bound for extreme values than…

math.NT2026

Extreme values of quadratic Hecke $L$ -functions

Zikang Dong, Long Liu

We study large values of quadratic Hecke $L$ -functions in the conductor aspect. Let $K$ be a fixed number field, and assume GRH for its finite-order Hecke $L$ -functions. In a fixed…

math.NT2026

Large zeta sums and zeros of the Riemann zeta function

Zikang Dong, Ruihua Wang, Weijia Wang +1

For real $t$ and $x \geq 1$ , set \[ S(x,t)=\sum_{n\le x} n^{\ii t}. \] We prove an unconditional inverse theorem relating large values of $S (x, t)$ , with $∣ t ∣$ large, to zeros of the…

math.NT2026

Large values of quadratic character sums

Zikang Dong, Ruihua Wang, Weijia Wang +2

In this paper, we investigate large values of quadratic Dirichlet character sums. We prove new Omega results for both short and long quadratic character sums under the assumption o…

math.NT2026

Extreme values of quadratic Dirichlet $L$ -functions with prime-related moduli

Zikang Dong, Weijia Wang, Hao Zhang +1

In this paper, we show a new lower bound for extreme values of quadratic Dirichlet $L$ -functions with prime-related moduli, which generalizes the work of Darbar and Maiti in 2025,…

math.NT2026

Extreme values of quadratic Dirichlet $L$ -functions

Zikang Dong, Weijia Wang, Hao Zhang +1

In this paper, we investigate extreme values of quadratic Dirichlet $L$ -functions at the central point. We provide new extreme values of $L (\frac{1}{2}, χ_{d})$ as $d$ is large, which imp…

math.NT2026

Finite $q$ -multiple harmonic sums at roots of unity: Symmetrized identities for $1$ - $2$ index multisets

Zikang Dong, Takao Komatsu

Closed-form results for finite $q$ -multiple harmonic sums are abundant for uniformly repeated indices, whereas mixed-weight tuples pose substantial combinatorial challenges. Buildi…

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

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

Large quadratic character sums

Zikang Dong, Yanbin Zhang

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

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,…

math.NT2025

Large values of quadratic Dirichlet $L$ -functions near the central point

Zikang Dong, Zhonghua Li, Yutong Song +1

In this paper, we investigate the conditional large values of the quadratic Dirichlet $L$ -functions near the central point $s = 1/2$ . When $σ$ closes to $1/2$ within a suitable range…

math.NT2025

Large values of character sums with multiplicative coefficients

Zikang Dong, Zhonghua Li, Yutong Song +1

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

Extreme values of Dirichlet L-functions on the critical line with a growing prime modulus

Extreme values of quadratic Hecke L-functions

Large zeta sums and zeros of the Riemann zeta function

Large values of quadratic character sums

Extreme values of quadratic Dirichlet L-functions with prime-related moduli

Extreme values of quadratic Dirichlet L-functions

Finite q-multiple harmonic sums at roots of unity: Symmetrized identities for 1-2 index multisets

Large values of quadratic character sums revisited

Note on large quadratic character sums

Large quadratic character sums with multiplicative coefficients

Large values of Dirichlet polynomials with multiplicative coefficients

Large character sums with multiplicative coefficients

Large quadratic character sums

Quadratic character sums with multiplicative coefficients

Large values of quadratic Dirichlet L-functions near the central point

Large values of character sums with multiplicative coefficients

Extreme values of Dirichlet $L$ -functions on the critical line with a growing prime modulus

Extreme values of quadratic Hecke $L$ -functions

Extreme values of quadratic Dirichlet $L$ -functions with prime-related moduli

Extreme values of quadratic Dirichlet $L$ -functions

Finite $q$ -multiple harmonic sums at roots of unity: Symmetrized identities for $1$ - $2$ index multisets

Large values of quadratic Dirichlet $L$ -functions near the central point