Asymptotics for moments of certain cotangent sums for arbitrary exponents

TL;DR

This paper extends the asymptotic analysis of moments of specific cotangent sums, originally established for integer exponents, to include arbitrary positive real exponents, broadening the understanding of their behavior.

Contribution

It introduces a generalized approach to asymptotics of cotangent sum moments for any positive real exponents, expanding previous integer-based results.

Findings

Extended asymptotic formulas to real exponents

Broadened understanding of cotangent sum behavior

Connected results to Estermann and Riemann zeta functions

Abstract

In this paper we extend a result on the asymptotics of moments of certain cotangent sums associated to the Estermann and Riemann zeta functions established in a previous paper for integer exponents to arbitrary positive real exponents.