Effective uniform approximation by $L$-functions in the Selberg class

TL;DR

This paper extends effective universality results from the Riemann zeta-function to a broader class of L-functions within the Selberg class, providing new uniform approximation techniques.

Contribution

It generalizes Voronin's effective denseness theorem to Selberg class L-functions under certain conditions, broadening the scope of universality results.

Findings

Generalization of Voronin's theorem to Selberg class

Effective uniform approximation results for L-functions

Broader applicability of universality principles

Abstract

Recently, Garunk\v{s}tis, Laurin\v{c}ikas, Matsumoto, J. & R. Steuding showed an effective universality-type theorem for the Riemann zeta-function by using an effective multi-dimensional denseness result of Voronin. We will generalize Voronin's effective result and their theorem to the elements of the Selberg class satisfying some conditions.