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A NEW UPPER BOUND FOR $\vert \zeta (1+ it)\vert $

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  13 June 2013

TIMOTHY TRUDGIAN
TIMOTHY TRUDGIAN*
Affiliation:
Mathematical Sciences Institute, The Australian National University, ACT 0200, Australia email [email protected]
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Abstract

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It is known that $\zeta (1+ it)\ll \mathop{(\log t)}\nolimits ^{2/ 3} $ when $t\gg 1$. This paper provides a new explicit estimate $\vert \zeta (1+ it)\vert \leq \frac{3}{4} \log t$, for $t\geq 3$. This gives the best upper bound on $\vert \zeta (1+ it)\vert $ for $t\leq 1{0}^{2\cdot 1{0}^{5} } $.

Keywords

Riemann zeta-functioncritical stripexponential sums

MSC classification

Secondary: 11M06: $zeta (s)$ and $L(s, chi)$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 259 - 264
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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