On the growth of the L^p norm of the Riemann zeta-function on the line Re(s)=1

2021/07/30 by Johan Andersson, Andersson, Johan
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2107.14748

openalex publication_date 2021/07/30 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28

Abstract

We prove that if δ>0 and p is real then sup_T ∫_T^T+δ |ζ(1+it)|^p dt 1) which with the exception of an additional log log log T factor in the second estimate coincides with conditional (under the Riemann hypothesis) order estimates. We also prove weaker unconditional order estimates.

Citations

• Voronin universality on the abscissa of absolute convergence

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