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Smooth-automorphic forms and smooth-...

Grobner, Harald.

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Smooth-automorphic forms and smooth-automorphic representations /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Smooth-automorphic forms and smooth-automorphic representations // Harald Grobner, University of Vienna, Austria.
Author:	Grobner, Harald.
Published:	Hackensack, NJ :World Scientific, : c2023.,
Description:	xviii, 243 p. ;24 cm.
[NT 15003449]:	Basic notions and concepts from functional analysis ("local") -- Representations of local groups - the very basics -- Langlands classification : step 1 - what to classify? -- Langlands classification : step 2 -- Langlands classification : step 3 -- Special representations : part 1 -- Special representations : part 2 -- Basic notions and concepts from functional analysis ("global") -- First adelic steps -- Representations of global groups -- the very basics -- Automorphic forms and smooth-automorphic forms -- Automorphic representations and smooth-automorphic representations -- Cuspidality and square-integrability -- Parabolic support -- Cuspidal support.
Subject:	Automorphic functions. -
ISBN:	9789811246166

Smooth-automorphic forms and smooth-automorphic representations /
Grobner, Harald.

Smooth-automorphic forms and smooth-automorphic representations /Harald Grobner, University of Vienna, Austria. - Hackensack, NJ :World Scientific,c2023. - xviii, 243 p. ;24 cm. - Series on number theory and its applications,vol. 171793-3161 ;. - Series on number theory and its applications ;vol. 17..

Includes bibliographical references and index.

Basic notions and concepts from functional analysis ("local") -- Representations of local groups - the very basics -- Langlands classification : step 1 - what to classify? -- Langlands classification : step 2 -- Langlands classification : step 3 -- Special representations : part 1 -- Special representations : part 2 -- Basic notions and concepts from functional analysis ("global") -- First adelic steps -- Representations of global groups -- the very basics -- Automorphic forms and smooth-automorphic forms -- Automorphic representations and smooth-automorphic representations -- Cuspidality and square-integrability -- Parabolic support -- Cuspidal support.

"This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F. Our approach to automorphic representations differs from the usual literature: We do not consider "K-finite" automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of "smooth-automorphic forms" is intrinsic to the group scheme G/F. This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G. Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail"--

ISBN: 9789811246166US88.00

LCCN: 2023008551Subjects--Topical Terms:

576005
Automorphic functions.

LC Class. No.: QA353.A9 / G76 2023

Dewey Class. No.: 515/.9

Smooth-automorphic forms and smooth-automorphic representations /
LDR:02549cam a2200229 a 4500 001 2321832
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008 231027s2023 nju b 001 0 eng d
010 $a 2023008551
020 $a 9789811246166 $q (hbk.) : $c US88.00
020 $z 9789811246173 $q (ebook for institutions)
020 $z 9789811246180 $q (ebook for individuals)
040 $a LBSOR $b eng $e rda $c LBSOR $d DLC
042 $a pcc
050 0 0 $a QA353.A9 $b G76 2023
082 0 0 $a 515/.9 $2 23/eng/20230605
100 1 $a Grobner, Harald. $3 3645429
245 1 0 $a Smooth-automorphic forms and smooth-automorphic representations / $c Harald Grobner, University of Vienna, Austria.
260 # $a Hackensack, NJ : $b World Scientific, $c c2023.
300 $a xviii, 243 p. ; $c 24 cm.
490 1 $a Series on number theory and its applications, $x 1793-3161 ; $v vol. 17
504 $a Includes bibliographical references and index.
505 0 # $a Basic notions and concepts from functional analysis ("local") -- Representations of local groups - the very basics -- Langlands classification : step 1 - what to classify? -- Langlands classification : step 2 -- Langlands classification : step 3 -- Special representations : part 1 -- Special representations : part 2 -- Basic notions and concepts from functional analysis ("global") -- First adelic steps -- Representations of global groups -- the very basics -- Automorphic forms and smooth-automorphic forms -- Automorphic representations and smooth-automorphic representations -- Cuspidality and square-integrability -- Parabolic support -- Cuspidal support.
520 # $a "This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F. Our approach to automorphic representations differs from the usual literature: We do not consider "K-finite" automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of "smooth-automorphic forms" is intrinsic to the group scheme G/F. This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G. Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail"-- $c Provided by publisher.
650 # 0 $a Automorphic functions. $3 576005
650 # 0 $a Automorphic forms. $3 576006
830 0 $a Series on number theory and its applications ; $v vol. 17. $3 3645430