The explicit upper bound of the multiple integral of S(t) on the Riemann Hypothesis

2012/10/10 by Takahiro Wakasa, Wakasa, Takahiro
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1210.3097

arxiv created 2012/10/11 · openalex publication_date 2012/10/11 · arxiv updated 2012/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove explicit upper bounds of the function S_m(T), defined by the repeated integration of the argument of the Riemann zeta-function. The explicit upper bound of S(T) and S₁(T) have already been obtained by A. Fujii. Our result is a generalization of Fujii's results.

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