Application of Meyer's theorem on quasicrystals to exponential polynomials and Dirichlet series

TL;DR

This paper establishes a criterion for certain Dirichlet series with real zeros to be finite sine products, utilizing Meyer's theorem on quasicrystals, bridging number theory and aperiodic order.

Contribution

It introduces a novel application of Meyer's theorem to characterize Dirichlet series with specific zero distributions as finite sine products.

Findings

Provides a necessary and sufficient condition for Dirichlet series to be finite sine products.

Connects Meyer's theorem on quasicrystals with properties of exponential polynomials.

Offers insights into the structure of Dirichlet series with real zeros.

Abstract

A simple necessary and sufficient condition is given for an absolutely convergent Dirichlet series with imaginary exponents and only real zeros to be a finite product of sines. The proof is based on Meyer's theorem on quasicrystals.