The order of magnitude for moments for certain cotangent sums

TL;DR

This paper determines the precise growth rate of moments for certain cotangent sums, providing the exact order of magnitude and analyzing moments of specific orders, advancing understanding of their asymptotic behavior.

Contribution

The authors establish the true order of magnitude for the moments of cotangent sums, resolving a previously open question and extending analysis to specific moment orders.

Findings

Exact order of magnitude of moments determined

Moments of order 2k between fixed multiples of (2k)!/π^{2k} analyzed

Provides asymptotic growth rates for cotangent sum moments

Abstract

We settle a question on the rate of growth of the moments of cotangent sums considered by the authors in their previous papers [8], [9]. We even obtain the true order of magnitude of these moments. We include as well the moments of order $2k$ between fixed multiples of $(2k)!/\pi^{2k}$.