On the Sidon Constant for Dirichlet Polynomials

TL;DR

This paper refines the bounds on the Sidon constant for Dirichlet polynomials by providing explicit error estimates and improving the upper bound with a logarithmic factor, enhancing understanding of their asymptotic behavior.

Contribution

It supplies explicit lower bounds and improves the upper bounds for the Sidon constant, making the asymptotic estimates more precise.

Findings

Explicit lower bounds for the Sidon constant are provided.

The upper bound is improved by a factor involving triple logarithms.

Enhanced asymptotic understanding of Dirichlet polynomial behavior.

Abstract

We estimate the error term in the asymptotic formula of the Sidon constant for (ordinary) Dirichlet polynomials by providing explicit lower and upper bounds. The lower bound is already implicitly known, but we supply the necessary computations to make it explicit. The upper bound is improved by a factor of $\log\log\log{x}/\sqrt{\log\log{x}}$.