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Automorphic Functions, Poincaré Series, and Conformal Fields on Riemann Surfaces
Author(s) -
Rühl W.
Publication year - 1988
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190361203
Subject(s) - automorphic l function , automorphic form , langlands–shahidi method , poincaré series , mathematics , conformal map , series (stratigraphy) , pure mathematics , riemann surface , poisson summation formula , riemann hypothesis , representation theory , eisenstein series , langlands program , mathematical analysis , fourier transform , modular form , paleontology , biology
Poincaré series and automorphic functions for SU (1, 1) and a discrete subgroup Γ are studied with harmonic analysis. We consider automorphic functions on the open unit circle with general “spin label” m and their decomposition into irreducible automorphic functions by means of the Plancherel formula. These automorphic functions are bijectively mapped onto automorphic distributions on the boundary of the unit circle by meam of the Poisson kernel. The exponent of convergence of Poincaré series is expressed in representation theory language. The results are applied to two‐point functions of conformal fields.