Zeta Functions on Arithmetic Surfaces

2013/11/27 by Thomas Oliver, Oliver, Thomas
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1311.6964

openalex publication_date 2013/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Related

• Mean-periodicity and zeta functions
• Equalities, congruences, and quotients of zeta functions in Arithmetic Mirror Symmetry
• Two dimensional adelic analysis and cuspidal automorphic representations of GL(2)
• Special Uniformity of Zeta Functions I. Geometric Aspect
• Automorphicity and Mean-Periodicity