Universality for the iterated integrals of logarithms of $L$-functions in the Selberg class

TL;DR

This paper proves a universality theorem for the iterated integrals of logarithms of $L$-functions within the Selberg class, demonstrating their approximation capabilities on certain lines parallel to the real axis.

Contribution

It establishes the universality property for a new class of functions derived from $L$-functions in the Selberg class, extending previous universality results.

Findings

Universality holds for iterated integrals of logarithms of $L$-functions.

The theorem applies on lines parallel to the real axis.

This extends the scope of universality in analytic number theory.

Abstract

We prove the universality theorem for the iterated integrals of logarithms of $L$-functions in the Selberg class on some line parallel to the real axis.