On Large Values of |ζ(σ+\rm it)|

2021/10/06 by Zikang Dong, Bin Wei, Dong, Zikang +1
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.04278

openalex publication_date 2021/10/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We investigate the extreme values of the Riemann zeta function ζ(s). On the 1-line, we obtain a lower bound evaluation max_t∈[1,T]|ζ(1+ıt)|≥ \rm e^γ(log₂T+log₃T+c), with an effective constant c which improves the result of Aistleitner, Mahatab and Munsch. In the half-critical strip 1/2

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