Holomorphic automorphic forms and cohomology /

"We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. We use Knopp's generalization of this integral to real weights,...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Bruggeman, Roelof W., 1944- (Author), Choie, YoungJu (Author), Diamantis, Nikolaos, 1970- (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, RI : American Mathematical Society, 2018.
Series:Memoirs of the American Mathematical Society ; no. 1212.
Subjects:
Algebraic topology.
Topologie algébrique.
MATHEMATICS > Algebra > Intermediate.
Topología
Algebraic topology
Online Access:Texto completo
Table of Contents:
  • Introduction
  • pt. 1 Cohomology with values in holomorphic functions
  • Definitions and notations
  • Modules and cocycles
  • The image of automorphic forms in cohomology
  • One-sided averages
  • pt. 2 Harmonic Functions
  • Harmonic functions and cohomology
  • Boundary germs
  • Polar harmonic functions
  • pt. 3 Cohomology with values in analytic boundary germs
  • Highest weight spaces of analytic boundary germs
  • Tesselation and cohomology
  • Boundary germ bohomology and automorphic forms
  • Automorphic forms of integral weights at least 2 and analytic boundary germ cohomology
  • pt. 4 Miscellaneous
  • Isomorphisms between parabolic cohomology groups
  • Cocycles and singularities
  • Quantum automorphic forms
  • Remarks on the literature.

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