Selberg's orthonormality conjecture and joint universality of L-functions

TL;DR

This paper introduces a novel approach leveraging the orthonormality of Dirichlet series coefficients within the Selberg class to establish joint universality of L-functions.

Contribution

It presents a new method connecting orthonormality relations to the proof of joint universality for L-functions in the Selberg class.

Findings

Established a link between orthonormality and universality

Proved joint universality using the new approach

Enhanced understanding of L-functions in the Selberg class

Abstract

In the paper we introduce the new approach how to use an orthonormality relation of coefficients of Dirichlet series defining given L-functions from the Selberg class to prove joint universality.