Zeta Functions on Arithmetic Surfaces

Abstract

We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called mean-periodicity correspondence, which is comparable to the better known automorphicity conjectures for the generic fibre.

28 pages. Numerous corrections from previous versions, and greater emphasis on exposition

References in corpus (4)

• An introduction to higher dimensional local fields and adeles
• Fubini's theorem and non-linear change of variables over a two-dimensional local field
• Computing $L$-functions and semistable reduction of superelliptic curves
• Automorphicity and Mean-Periodicity

Cited by in corpus (1)

• Automorphicity and Mean-Periodicity