17 papers · 1 filter
Extreme values of Dirichlet -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 -functions on the critical line with a growing prime modulus. Our result yields a larger lower bound for extreme values than…
Large values of the Hurwitz zeta function with rational parameter
Qiyu Yang, Shengbo Zhao, Guang-Liang Zhou
In this paper, we establish lower bounds for large values of the Hurwitz zeta function with rational parameter when the real part . These results improve the earlier…
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…
Extreme values of quadratic Dirichlet -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 -functions with prime-related moduli, which generalizes the work of Darbar and Maiti in 2025,…
Extreme values of quadratic Dirichlet -functions
Zikang Dong, Weijia Wang, Hao Zhang +1
In this paper, we investigate extreme values of quadratic Dirichlet -functions at the central point. We provide new extreme values of as is large, which imp…
Extreme values of derivatives of Dirichlet -functions
Xinghua Cui, Zhifeng Peng, Yutong Song +1
In this paper, we establish lower bounds for extreme values of derivatives of Dirichlet \(L\)-functions in the range \(1/2<σ<1\). Compared with the work of Aistleitner, Mahatab, Mu…
Some Omega results for Dirichlet -functions
Qiyu Yang, Shengbo Zhao
Motivated by the first author's earlier work in 2024, we use the resonance method to establish some Omega results for Dirichlet -functions, extending the previous results.
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…
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…
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…
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 , where for large . We prove an impro…
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 . We prove a new Omega result in the region $\exp((\l…
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 . For a positive number within a suitable range,…
Large values of quadratic Dirichlet -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 -functions near the central point . When closes to within a suitable range…
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 . We prove an Omega result in the region $\exp((\lo…
Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field
Zhonghua Li, Yutong Song, Qiyu Yang +1
In this paper, we establish a lower bound for the maximum of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double version convol…
Omega Theorems for Logarithmic Derivatives of Zeta and L-functions Near the 1-line
Zhonghua Li, Shengbo Zhao
We establish an omega theorem for logarithmic derivative of the Riemann zeta function near the 1-line by resonance method. We show that the inequality $\left| ζ^{\prime}\left(σ_A+i…