The effect of repeated differentiation on $L$-functions
Number Theory
2018-05-15 v2
Abstract
We show that under repeated differentiation, the zeros of the Selberg -function become more evenly spaced out, but with some scaling towards the origin. We do this by showing the high derivatives of the -function converge to the cosine function, and this is achieved by expressing a product of Gamma functions as a single Fourier transform.
Keywords
Cite
@article{arxiv.1803.10001,
title = {The effect of repeated differentiation on $L$-functions},
author = {Jos Gunns and Christopher Hughes},
journal= {arXiv preprint arXiv:1803.10001},
year = {2018}
}
Comments
Corrected minor typos; added a reference