Families of Automorphic Forms
Buch in deiner Nähe kaufen
Beschreibung
This text gives a systematic treatment of real analytic automorphic forms on the upper half plane for general confinite discrete subgroups. It introduces the main ideas then offers many examples that clarify the general theory and results developed therefrom.
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)).
New material so far mostly available in articles only
Autor*in
Roelof W. Bruggeman
Themen in »Families of Automorphic Forms«
Analytic automorphic forms Colin de Verdiere Discrete cofinite subgroups Eigenvalue Eisenstein series Modular group Multiplier system Poincare series Singularities automorphic forms function operator review spectral theory transformation
Stimmen zu »Families of Automorphic Forms«
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
()