English

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

Number Theory 2022-06-28 v1

Abstract

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

Keywords

Cite

@article{arxiv.2006.16884,
  title  = {On the Vertical Distribution of Values of $L$-functions in the Selberg Class},
  author = {Athanasios Sourmelidis and Teerapat Srichan and Jörn Steuding},
  journal= {arXiv preprint arXiv:2006.16884},
  year   = {2022}
}

Comments

28 pages