On the Vertical Distribution of Values of $L$-functions in the Selberg Class

TL;DR

This paper derives explicit formulas for the $eta$-points of $L$-functions in the Selberg class, extends Littlewood's theorem to these points, and establishes their uniform distribution and universality properties.

Contribution

It introduces explicit formulas for $eta$-points of Selberg class $L$-functions and extends classical zero distribution results to these points.

Findings

Explicit formulas for $eta$-points of $L$-functions

Extension of Littlewood's theorem to $eta$-points

Discreteness and universality of $eta$-points

Abstract

We prove explicit formulae for $\alpha$-points of $L$-functions from the Selberg class. Next we extend a theorem of Littlewood on the vertical distribution of zeros of the Riemann zeta-function $\zeta(s)$ to the case of $\alpha$-points of the aforementioned $L$-functions. This result implies the uniform distribution of subsequences of $\alpha$-points and from this a discrete universality theorem in the spirit of Voronin is derived.