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MARC 21

Families of Automorphic Forms
Tag	Description
020	$a9783034603362$9978-3-0346-0336-2
082	$a515.8$223
099	$aOnline resource: Springer
100	$aBruggeman, Roelof W.
245	$aFamilies of Automorphic Forms$h[EBook] /$cby Roelof W. Bruggeman.
260	$aBasel :$bBirkhäuser Basel :$bImprint: Birkhäuser,$c1994.
300	$aX, 318 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aModern Birkhäuser Classics
505	$aModular introduction -- Modular introduction -- General theory -- Automorphic forms on the universal covering group -- Discrete subgroups -- Automorphic forms -- Poincaré series -- Selfadjoint extension of the Casimir operator -- Families of automorphic forms -- Transformation and truncation -- Pseudo Casimir operator -- Meromorphic continuation of Poincaré series -- Poincaré families along vertical lines -- Singularities of Poincaré families -- Examples -- Automorphic forms for the modular group -- Automorphic forms for the theta group -- Automorphic forms for the commutator subgroup.
520	$aAutomorphic 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)).
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aModern Birkhäuser Classics
856	$uhttp://dx.doi.org/10.1007/978-3-0346-0336-2