English

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.

Keywords

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

R2 v1 2026-06-21T16:43:55.028Z