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pro vyhledávání: '"DONG, ZIKANG"'
We study the conditional upper bounds and extreme values of derivatives of the Riemann zeta function and Dirichlet $L$-functions near the 1-line. Let $\ell$ be a fixed natural number. We show that, if $|\sigma-1|\ll1/\log_2t$, then $|\zeta^{(\ell)}(\
Externí odkaz:
http://arxiv.org/abs/2312.12199
In this article, we investigate the behaviour of values of zeta sums $\sum_{n\le x}n^{it}$ when $t$ is large. We show some asymptotic behaviour and Omega results of zeta sums, which are analogous to previous results of large character sums $\sum_{n\l
Externí odkaz:
http://arxiv.org/abs/2310.13383
In this article, we study the distribution of large quadratic character sums. Based on the recent work of Lamzouri~\cite{La2022}, we obtain the structure results of quadratic characters with large character sums.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2306.06355
In this article, we study the distribution of values of Dirichlet $L$-functions, the distribution of values of the random models for Dirichlet $L$-functions, and the discrepancy between these two kinds of distributions. For each question, we consider
Externí odkaz:
http://arxiv.org/abs/2209.11059
Autor:
Dong, Zikang, Wei, Bin
We investigate the large values of the derivatives of the Riemann zeta function $\zeta(s)$ on the 1-line. We give a larger lower bound for $\max_{t\in[T,2T]}|\zeta^{(\ell)}(1+{\rm i} t)|$, which improves the previous result established by Yang.
Externí odkaz:
http://arxiv.org/abs/2203.16086
Autor:
Dong, Zikang
In this article, we study the distribution of large values of the Riemann zeta function on the 1-line. We obtain an improved density function concerning large values, holding in the same range as that given by Granville and Soundararajan.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/2110.03293
Autor:
Dong, Zikang, Wei, Bin
We investigate the extreme values of the Riemann zeta function $\zeta(s)$. On the 1-line, we obtain a lower bound evaluation $$\max_{t\in[1,T]}|\zeta(1+\i t)|\ge {\rm e}^\gamma(\log_2T+\log_3T+c),$$ with an effective constant $c$ which improves the r
Externí odkaz:
http://arxiv.org/abs/2110.04278
Akademický článek
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Akademický článek
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Autor:
DONG, ZIKANG, WEI, BIN
Publikováno v:
Bulletin of the Australian Mathematical Society; Oct2023, Vol. 108 Issue 2, p217-223, 7p
