On the maximum of cotangent sums related to the Riemann Hypothesis in rational numbers in short intervals

TL;DR

This paper studies the maximum values of cotangent sums over rational numbers in short intervals, which are relevant to the Nyman-Beurling criterion for the Riemann Hypothesis, providing insights into their behavior.

Contribution

It investigates the maximum of cotangent sums over rational numbers in short intervals, advancing understanding of their role in the Riemann Hypothesis.

Findings

Identifies bounds for cotangent sums in short intervals

Analyzes the distribution of maximum cotangent sums

Provides new estimates related to the Nyman-Beurling criterion

Abstract

Cotangent sums play a significant role in the Nyman-Beurling criterion for the Riemann Hypothesis. Here we investigate the maximum of the values of these cotangent sums over various sets of rational numbers in short intervals.