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 language | English |
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Pages (from-to) | 199-233 |
Number of pages | 35 |
Journal | Algebra i Analiz |
Volume | 27 |
Issue number | 6 |
DOIs | |
Publication status | Published - 30 Sept 2016 |
Keywords
- Scheme of finite type; zeta function; local field; Hasse--Weil L-function; complete discrete valuation field; adeles.