An explicit upper bound for |? (1+it)|

被引：7
作者：
Patel, Dhir [1 ]
机构：
[1] Ohio State Univ, Dept Math, 231 West 18th Ave, Columbus, OH 43210 USA
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2022年 / 33卷 / 05期
关键词：
van der Corput estimate; Exponential sums; Riemann zeta function; van der Corput test; Explicit derivative tests; Cheng-Graham lemma; Explicit estimate for Riemann zeta function; Explicit van der Corput bound; RIEMANN ZETA-FUNCTION; FORMULA;
D O I：
10.1016/j.indag.2022.04.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we provide an explicit bound for |zeta (1 + it)| in the form of |zeta (1 + it)| <= min(log t, 2 log t + 1.93, 1 1 5 log t +44.02). This improves on the current best-known explicit bound of |zeta(1 + it)| & LE; 62.6(log t)2/3 up until t of the magnitude 10107.(c) 2022 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1012 / 1032
页数：21
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