A note on the maximum of the Riemann zeta function on the 1‐line

Winston Heap

Type: Article

Publication Date: 2020-06-22

Citations: 1

DOI: https://doi.org/10.1112/blms.12382

Abstract

We investigate the relationship between the maximum of the zeta function on the 1-line and the maximal order of S ( t ) , the error term in the number of zeros up to height t. We show that the conjectured upper bounds on S ( t ) along with the Riemann hypothesis imply a conjecture of Littlewood that max t ∈ [ 1 , T ] | ζ ( 1 + i t ) | ∼ e γ log log T . The relationship in the region 1 / 2 < σ < 1 is also investigated.

Locations

Bulletin of the London Mathematical Society - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (7)

Action	Title	Year	Authors
+	Extreme values of the Riemann zeta function	1977	Hugh L. Montgomery
+	Mathematical Notes (5): On the Function 1/ζ(1+<i>ti</i> )	1928	J. E. Littlewood
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown
+ PDF Chat	Note on the Resonance Method for the Riemann Zeta Function	2018	Andriy Bondarenko Kristian Seip
+ PDF Chat	Extreme values of the Riemann zeta function and its argument	2018	Andriy Bondarenko Kristian Seip
+ PDF Chat	The maximum size of L-functions	2007	David W. Farmer S. M. Gonek C. P. Hughes
+ PDF Chat	Extreme Values of the Riemann Zeta Function on the 1-Line	2017	Christoph Aistleitner Kamalakshya Mahatab Marc Munsch