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A NEW UPPER BOUND FOR
$\vert \zeta (1+ it)\vert $
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 2 / April 2014
- Published online by Cambridge University Press:
- 13 June 2013, pp. 259-264
- Print publication:
- April 2014
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- Article
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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} } $.
