An Explicit Upper Bound for |ζ(1+it)|

2020/09/02 by Dhir Patel, Patel, Dhir
Computer Science · Mathematics · #Coding theory and cryptography #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2009.00769

Abstract

In this paper we provide an explicit bound for |ζ(1+it)| in the form of |ζ(1+it)|≤ min(log t, (1)/(2)log t+1.93, (1)/(5)log t+44.02 ). This improves on the current best-known explicit bound of |ζ(1+it)|≤ 62.6(log t)^2/3 up until t of the magnitude 10¹⁰⁷.

Citations

• An improved upper bound for the argument of the Riemann zeta-function on the critical line II
• Zur Absch�tzung der Riemannschen Zetafunktion in der N�he der Vertikalen ?=1
• Über die Nullstellen der Riemannschen Zetafunktion

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