Modern Birkhäuser Classics

Families of Automorphic Forms

Authors: Bruggeman, Roelof W.

  • New material so far mostly available in articles only

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About this book

Automorphic forms on the upper half plane have been studied for a long time. Most attention has gone to the holomorphic automorphic forms, with numerous applications to number theory. Maass, [34], started a systematic study of real analytic automorphic forms. He extended Hecke’s relation between automorphic forms and Dirichlet series to real analytic automorphic forms. The names Selberg and Roelcke are connected to the spectral theory of real analytic automorphic forms, see, e. g. , [50], [51]. This culminates in the trace formula of Selberg, see, e. g. , Hejhal, [21]. Automorphicformsarefunctionsontheupperhalfplanewithaspecialtra- formation behavior under a discontinuous group of non-euclidean motions in the upper half plane. One may ask how automorphic forms change if one perturbs this group of motions. This question is discussed by, e. g. , Hejhal, [22], and Phillips and Sarnak, [46]. Hejhal also discusses the e?ect of variation of the multiplier s- tem (a function on the discontinuous group that occurs in the description of the transformation behavior of automorphic forms). In [5]–[7] I considered variation of automorphic forms for the full modular group under perturbation of the m- tiplier system. A method based on ideas of Colin de Verdi` ere, [11], [12], gave the meromorphic continuation of Eisenstein and Poincar´ e series as functions of the eigenvalue and the multiplier system jointly. The present study arose from a plan to extend these results to much more general groups (discrete co?nite subgroups of SL (R)).

Reviews

From reviews:

"It is made abundantly clear that this viewpoint, of families of automorphic functions depending on varying eigenvalue and multiplier systems, is both deep and fruitful." - MathSciNet


Table of contents (15 chapters)

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-0346-0336-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-0346-0335-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Families of Automorphic Forms
Authors
Series Title
Modern Birkhäuser Classics
Copyright
1994
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-0346-0336-2
DOI
10.1007/978-3-0346-0336-2
Softcover ISBN
978-3-0346-0335-5
Series ISSN
2197-1803
Edition Number
1
Number of Pages
X, 318
Additional Information
Originally published in the series: Monographs in Mathematics Vol 88
Topics