Period functions and cotangent sums

S Bettin, JB Conrey

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

32 Citations (Scopus)

Abstract

We investigate the period function of ∑n=1∞σa(n)e(nz), showing it can be analytically continued to |argz| < π and studying its Taylor series. We use these results to give a simple proof of the Voronoi formula and to prove an exact formula for the second moments of the Riemann zeta function. Moreover, we introduce a family of cotangent sums, functions defined over the rationals, that generalize the Dedekind sum and share with it the property of satisfying a reciprocity formula.
Translated title of the contributionPeriod functiona and cotangent sums
Original languageEnglish
Pages (from-to)215-242
Number of pages28
JournalAlgebra and Number Theory
Volume7
Issue number1
DOIs
Publication statusPublished - 2013

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