15 papers
Large zeta sums and zeros of the Riemann zeta function
Zikang Dong, Ruihua Wang, Weijia Wang +1
For real and , set \[ S(x,t)=\sum_{n\le x} n^{\ii t}. \] We prove an unconditional inverse theorem relating large values of , with large, to zeros of the…
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…
Spectral eigenvalue set of self-similar measures associated with product-form Hadamard triples
Xin Yang, Wei-Jie Wang
Previously, An \cite{AL01} showed that the self-similar measure generated by a product-form Hadamard triple is a spectral measure. In this paper, we study its spectral eigenval…
Common Spectral Eigenvalue Spectra for Random Convolutions Generated by Hadamard Triples
Wei-Jie Wang, Xin Yang
Lu proved that the set constitutes a spectral eigenvalue set for , wher…
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…
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…
The Diophantine Frobenius Problem revisited
Yuchen Ding, Weijia Wang, Hao Zhang
Let and 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}…
Lower bounds for high moments of zeta sums
Zikang Dong, Weijia Wang, Hao Zhang
In this article, we investigate high moments of zeta sums . We show unconditional lower bounds for them.
Quaternionic Mahler measure
Weijia Wang, Hao Zhang
We introduce the quaternionic Mahler measure for non-commutative polynomials, extending the classical complex Mahler measure. We establish the existence of quaternionic Mahler meas…
On derivatives of zeta and -functions near the 1-line
Zikang Dong, Yutong Song, Weijia Wang +1
We study the conditional upper bounds and extreme values of derivatives of the Riemann zeta function and Dirichlet -functions near the 1-line. Let be a fixed natural numb…
Large zeta sums
Zikang Dong, Weijia Wang, Hao Zhang
In this article, we investigate the behaviour of values of zeta sums when is large. We show some asymptotic behaviour and Omega results of zeta sums, whic…