Zeta Integrals on Arithmetic Surfaces

Thomas D Oliver

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

302 Downloads (Pure)


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
Issue number6
Publication statusPublished - 30 Sept 2016


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


Dive into the research topics of 'Zeta Integrals on Arithmetic Surfaces'. Together they form a unique fingerprint.

Cite this