Notes on the Poisson formula
Number Theory
2010-11-16 v1 Algebraic Geometry
Representation Theory
Abstract
These notes are a part of my lectures on representations of adelic groups attached to two-dimensional schemes. They contain a study of the one-dimensional case as a preliminary step to the case of dimension two. We consider the following issues: the Tate--Iwasawa method for algebraic curves; a discrete version and holomorphic duality; the Poisson formula and residues; explicit formulas; relation with the Artin representation; analogues for the number fields. With appendix on the Dedekind zeta-functions by Irina Rezvjakova.
Cite
@article{arxiv.1011.3392,
title = {Notes on the Poisson formula},
author = {A. N. Parshin},
journal= {arXiv preprint arXiv:1011.3392},
year = {2010}
}
Comments
46 pages,submitted to the Saint-Petersburg mathematical Journal