The error for the second moment of cotangent sums related to the Riemann Hypothesis

TL;DR

This paper establishes a lower bound for the error term in the asymptotic analysis of the second moment of cotangent sums related to the Riemann Hypothesis, advancing understanding of their precise behavior.

Contribution

It provides a new lower bound for the error term in the second moment asymptotics of cotangent sums connected to the Riemann Hypothesis.

Findings

Established a lower bound for the error term

Enhanced understanding of cotangent sum moments

Refined asymptotic analysis related to the Riemann Hypothesis

Abstract

In various papers the authors have derived asymptotics for moments of certain cotangent sums related to the Riemann Hypothesis. S. Bettin has given an upper bound for the error term in these asymptotic results. In the present paper the authors establish a lower bound for the error term for the second moment.