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

2018/12/04 by Heap, Winston
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1812.01415

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+it)|∼ e^γloglog T. The relationship in the region 1/2

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