Arithmetic and Analysis of the series ∑_n=1^∞ (1)/(n) sin (x)/(n)

2020/09/27 by Roger Gay, Gay, Roger, Ahmed Sebbar +1
Mathematics · #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematics and Applications #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2009.14070

openalex publication_date 2020/09/27 · openalex created_date 2023/03/14 · openalex updated_date 2026/07/28

Abstract

In this paper we connect a celebrated theorem of Nyman and Beurling on the equivalence between the Riemann hypothesis and the density of some functional space in L²(0, 1) to a trigonometric series considered first by Hardy and Littlewood. We highlight some of its curious analytical and arithmetical properties.

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