Strong multiplicity one for the Selberg class

TL;DR

This paper investigates conditions under which functions in the Selberg class are uniquely determined by their coefficients at prime squares or their zeroes, advancing understanding of their structural properties.

Contribution

It introduces new criteria for identifying Selberg class functions based on coefficients at prime squares and zeroes, enhancing the uniqueness results in analytic number theory.

Findings

Unique determination of Selberg class functions from prime square coefficients

New criteria linking zeroes to function identification

Advancement in understanding the structure of the Selberg class

Abstract

We study the problem of determining elements of the Selberg class by information on the coefficents of the Dirichlet series at the squares of primes, or information about the zeroes of the functions.