Notes on the Poisson formula

Details Notes on the Poisson formula Notes on the Poisson formula

2010-11-15

arxiv.org/abs/1011.3392v1

Mathematics

Number Theory

46 pages,submitted to the Saint-Petersburg mathematical Journal

Scientific paper

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.

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