On the linear twist of degree 1 functions in the extended Selberg class

Giamila Zaghloul

On the linear twist of degree 1 functions in the extended Selberg class

Number Theory 2019-03-15 v1

Authors: Giamila Zaghloul

Abstract

Given a degree 1 function $F\in\mathcal{S}^{\sharp}$ and a real number $\alpha$ , we consider the linear twist $F(s,\alpha)$ , proving that it satisfies a functional equation reflecting $s$ into $1-s$ , which can be seen as a Hurwitz-Lerch type of functional equation. We also derive some results on the distribution of the zeros of the linear twist.

Keywords

extended selberg class degree 1 function linear twist functional equation zero distribution

Cite

@article{arxiv.1903.06145,
  title  = {On the linear twist of degree 1 functions in the extended Selberg class},
  author = {Giamila Zaghloul},
  journal= {arXiv preprint arXiv:1903.06145},
  year   = {2019}
}

Comments

12 pages

Related papers

View all related →