The effect of repeated differentiation on L-functions

Jos Gunns, Chris Hughes

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
194 Downloads (Pure)

Abstract

We show that under repeated differentiation, the zeros of the Selberg Ξ-function become more evenly spaced out, but with some scaling towards the origin. We do this by showing the high derivatives of the Ξ-function converge to the cosine function, and this is achieved by expressing a product of Gamma functions as a single Fourier transform.

Original languageEnglish
Pages (from-to)30-43
Number of pages14
JournalJournal of Number Theory
Volume194
Early online date22 Aug 2018
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Selberg class of L-functions

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