Cotangent sums related to the Riemann Hypothesis for various shifts of the argument

TL;DR

This paper explores the behavior of cotangent sums associated with the Riemann Hypothesis, focusing on how these sums vary with different argument shifts, contributing to the understanding of the Nyman-Beurling criterion.

Contribution

It investigates cotangent sums for various argument shifts, providing new insights into their properties related to the Riemann Hypothesis and the Nyman-Beurling criterion.

Findings

Identified patterns in cotangent sums for different argument shifts

Enhanced understanding of cotangent sums' role in the Nyman-Beurling criterion

Potential implications for approaches to the Riemann Hypothesis

Abstract

One of the approaches to the Riemann Hypothesis is the Nyman-Beurling criterion. Cotangent sums play a significant role. Here we investigate the values of these cotangent sums for various shifts of the argument.