The rate of growth of moments of certain cotangent sums

TL;DR

This paper investigates the growth rate of moments of specific cotangent sums linked to zeros of the Estermann zeta function, providing new insights and a simplified proof of their equidistribution.

Contribution

It determines the growth rate of moments of cotangent sums and offers a simpler proof of their equidistribution, advancing understanding of these sums' behavior.

Findings

Established the rate of growth of moments of cotangent sums.

Provided a simplified proof of equidistribution of these sums.

Connected cotangent sums to zeros of the Estermann zeta function.

Abstract

We consider cotangent sums associated to the zeros of the Estermann zeta function considered by the authors in their previous paper [5]. We settle a question on the rate of growth of the moments of these cotangent sums left open in [5], and obtain a simpler proof of the equidistribution of these sums.