Zeta Integrals on Arithmetic Surfaces

Thomas D Oliver

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

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Abstract

We utilise a form of "lifted" harmonic analysis on the non-locally compact analytic adele groups associated to arithmetic surfaces to develop an integral representation for their zeta function. We proceed by emulating Tate's thesis to study the elusive analytic properties of zeta functions. An adelic interpretation of a mean-periodicity condition, which is closely related to automorphicity of the generic fibre, is given.
Original languageEnglish
Pages (from-to)199-233
Number of pages35
JournalAlgebra i Analiz
Volume27
Issue number6
DOIs
Publication statusPublished - 30 Sep 2016

Keywords

  • Scheme of finite type; zeta function; local field; Hasse--Weil L-function; complete discrete valuation field; adeles.

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