Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operato...

Celý popis

Uloženo v:
Podrobná bibliografie
Hlavní autoři: Bruggeman, Roelof, Pohl, Anke Dorothea
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2023
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Number theory
Number theory-Data processing
infinite covolume
transfer operator
period functions
mixed cohomology
cohomology
automorphic forms
Hecke triangle groups
funnel forms
ISBN:9781470465452, 1470465450
ISSN:0065-9266, 1947-6221
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.
AbstractList We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.
View the abstract.
Author Bruggeman, Roelof
Pohl, Anke Dorothea
Author_xml – sequence: 1
  givenname: Roelof
  surname: Bruggeman
  fullname: Bruggeman, Roelof
– sequence: 2
  givenname: Anke Dorothea
  surname: Pohl
  fullname: Pohl, Anke Dorothea
BackLink https://cir.nii.ac.jp/crid/1130578968288909451$$DView record in CiNii
BookMark eNpVkU1r3DAQhtUmKd1N99B_IGgPzcGNRpL1cUyXzQcEcgm9Gtk7TsTa0lay0_z82NmFUhhmDvPMvPC-S3IaYkBCvgL7Ccyyyx77eAmSiw9kZbUBqZnUpbDsI1mAlbpQnMPJv50qZclPyYIxVRaWK3VGlpxxwQRIaz6RJQjLheSyhM9klbOvWcmNkoKVC-I3_glDO4Zm8DFkGlv6mFzILSb6sMfkhpgydWFLr8Yh9jHtn31Dr2PqM21jorfY7HA68S48dUhvUhz371_uQuuDH5Cu40vsxh6_kLPWdRlXx3lOfl9vHte3xf3Dzd366r5wYI1-LRoDxjqlZO3aUrEGhMYWQTtUqLSrDc4lBLeudDXjoJjRWyF0s1UoJBPn5OLw2OUd_s3PsRty9dJhHeMuV_85OrE_Duw-xT8j5qF6xxoMQ3Jdtfm1FkxpsDCj3w9o8L5q_NwBJg-1scpwYyyzk8MT9u2o3ufqqAmsmpOt5mSrOVnxBiIFivg
ContentType eBook
Book
Copyright Copyright 2023 American Mathematical Society
Copyright_xml – notice: Copyright 2023 American Mathematical Society
DBID RYH
DEWEY 512.7
DOI 10.1090/memo/1423
DatabaseName CiNii Complete
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 9781470475390
1470475391
EISSN 1947-6221
Edition 1
ExternalDocumentID 9781470475390
EBC30671910
BD03747303
10_1090_memo_1423
GroupedDBID --Z
-~X
123
4.4
85S
ABPPZ
ACNCT
ACNUO
AEGFZ
AENEX
ALMA_UNASSIGNED_HOLDINGS
DU5
P2P
RMA
WH7
YNT
YQT
38.
AABBV
ABARN
ABQPQ
ADVEM
AERYV
AFOJC
AHWGJ
AJFER
BBABE
CZZ
GEOUK
RYH
ID FETCH-LOGICAL-a1987x-c8189a664baf560c137efe17ae6e67ab8eb8eb3329a5ab0216087d337cd6e3403
ISBN 9781470465452
1470465450
ISICitedReferencesCount 0
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=0000061315&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0065-9266
IngestDate Fri Nov 08 02:35:25 EST 2024
Wed Nov 26 03:15:18 EST 2025
Thu Jun 26 22:58:17 EDT 2025
Thu Aug 14 15:25:32 EDT 2025
IsPeerReviewed true
IsScholarly true
Keywords infinite covolume
transfer operator
period functions
mixed cohomology
cohomology
automorphic forms
Hecke triangle groups
funnel forms
LCCN 2023031498
LCCallNum_Ident QA241 .B784 2023
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-a1987x-c8189a664baf560c137efe17ae6e67ab8eb8eb3329a5ab0216087d337cd6e3403
Notes Includes bibliographical references (p. 165-167) and index
July 2023, volume 287, number 1423 (first of 6 numbers)
OCLC 1392342451
PQID EBC30671910
PageCount 186
ParticipantIDs askewsholts_vlebooks_9781470475390
proquest_ebookcentral_EBC30671910
nii_cinii_1130578968288909451
ams_ebooks_10_1090_memo_1423
PublicationCentury 2000
PublicationDate 2023.
PublicationDateYYYYMMDD 2023-01-01
PublicationDate_xml – year: 2023
  text: 2023.
PublicationDecade 2020
PublicationPlace Providence, Rhode Island
PublicationPlace_xml – name: Providence, Rhode Island
– name: Providence, RI
– name: Providence
PublicationSeriesTitle Memoirs of the American Mathematical Society
PublicationYear 2023
Publisher American Mathematical Society
Publisher_xml – name: American Mathematical Society
SSID ssib052864305
ssj0002915004
ssj0008047
Score 2.6633077
Snippet We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these...
View the abstract.
SourceID askewsholts
proquest
nii
ams
SourceType Aggregation Database
Publisher
SubjectTerms Number theory
Number theory-Data processing
TableOfContents Introduction -- Preliminaries, properties of period functions, and some insights -- Notations -- Elements from hyperbolic geometry -- Hecke triangle groups with infinite covolume -- Automorphic forms -- Principal series -- Transfer operators and period functions -- An intuition and some insights -- Semi-analytic cohomology -- Abstract cohomology spaces -- Modules -- Automorphic forms and cohomology -- Invariant eigenfunctions via a group cohomology -- Tesselation cohomology -- Extension of cocycles -- Surjectivity I: Boundary germs -- Surjectivity II: From cocycles to funnel forms -- Relation between cohomology spaces -- Proof of Theorem D -- Transfer operators and cohomology -- The map from functions to cocycles -- Real period functions and semi-analytic cocycles -- Complex period functions and semi-analytic cohomology -- Proof of Theorem E -- Proofs of Theorems A and B, and a recapitulation -- Parity -- The triangle group in the projective general linear group -- Odd and even funnel forms, cocycles, and period functions -- Isomorphisms with parity -- Complements and outlook -- Fredholm determinant of the fast transfer operator -- Outlook
Cover -- Title page -- Chapter 1. Introduction -- Motivational background -- Aim of this monograph -- Acknowledgement -- Part 1. Preliminaries, properties of period functions, and some insights -- Chapter 2. Notations -- Chapter 3. Elements from hyperbolic geometry -- 3.1. Models and isometries -- 3.2. Classification of isometries -- 3.3. Cusps, funnels, limit set, and ordinary points -- 3.4. Geodesics, resonances, and the Selberg zeta function -- 3.5. Intervals and rounded neighborhoods -- Chapter 4. Hecke triangle groups with infinite covolume -- Chapter 5. Automorphic forms -- 5.1. Funnel forms of different types -- 5.2. Fourier expansion -- Chapter 6. Principal series -- 6.1. Regularity at infinity -- 6.2. Presheaves and sheaves -- 6.3. Holomorphic extensions -- Chapter 7. Transfer operators and period functions -- 7.1. Discretizations and transfer operators -- 7.2. Slow transfer operators -- 7.3. Period functions -- 7.4. Real and complex period functions -- 7.5. Fast transfer operators -- 7.6. One-sided averages -- 7.7. Convergence and meromorphic extension of fast transfer operators -- 7.8. Spaces of complex period functions -- Chapter 8. An intuition and some insights -- Part 2. Semi-analytic cohomology -- Chapter 9. Abstract cohomology spaces -- 9.1. Standard group cohomology -- 9.2. Cohomology on an invariant set -- 9.3. Relation to parabolic cohomology spaces -- Chapter 10. Modules -- 10.1. Modules of semi-analytic functions -- 10.2. Submodules of semi-analytic vectors -- 10.3. Conditions on cocycles -- 10.4. Cohomological interpretation of the singularity condition -- Part 3. Automorphic forms and cohomology -- Chapter 11. Invariant eigenfunctions via a group cohomology -- Chapter 12. Tesselation cohomology -- 12.1. Choice of a tesselation, and cohomology -- 12.2. Relation to group cohomology -- 12.3. Mixed cohomology spaces
Chapter 13. Extension of cocycles -- Chapter 14. Surjectivity I: Boundary germs -- 14.1. Analytic boundary germs and semi-analytic modules -- 14.2. Cohomology classes attached to funnel forms -- 14.3. Representatives of boundary germs -- Chapter 15. Surjectivity II: From cocycles to funnel forms -- 15.1. From a cocycle to an invariant eigenfunction -- 15.2. A cocycle on an orbit of ordinary points -- 15.3. Isomorphisms -- Chapter 16. Relation between cohomology spaces -- Chapter 17. Proof of Theorem D -- From funnel forms to cocycle classes on the invariant set -- From cocycle classes on to funnel forms -- Proof of Theorem D -- Part 4. Transfer operators and cohomology -- Chapter 18. The map from functions to cocycles -- Chapter 19. Real period functions and semi-analytic cocycles -- Chapter 20. Complex period functions and semi-analytic cohomology -- Chapter 21. Proof of Theorem E -- Part 5. Proofs of Theorems A and B, and a recapitulation -- Part 6. Parity -- Chapter 22. The triangle group in the projective general linear group -- 22.1. Two actions of the projective general linear group -- 22.2. The triangle group -- Chapter 23. Odd and even funnel forms, cocycles, and period functions -- 23.1. Odd and even funnel forms -- 23.2. Odd and even cocycles -- 23.3. Odd and even period functions -- Chapter 24. Isomorphisms with parity -- Part 7. Complements and outlook -- Chapter 25. Fredholm determinant of the fast transfer operator -- Chapter 26. Outlook -- Bibliography -- Index of terminology -- List of notations -- Back Cover
Title Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
URI https://www.ams.org/memo/1423/
https://cir.nii.ac.jp/crid/1130578968288909451
https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=30671910
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9781470475390
Volume 287
WOSCitedRecordID wos0000061315&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Pb9MwFLZo4UBP_BSFDRnErQqz68yOr9sKSKCB0IDdIsdxSrQ2npp06p-_ZydxS3dAHJAqq4miWHlf4ve9Z7_PCL0jSS4KrlSUaQoBitE0SqROoswIIXKWM6q8uv4XcX6eXF7Kb91WjLXfTkBUVbLZyOv_CjWcA7Bd6ew_wB1uCifgP4AOLcAO7R4jDoddYt0Jazo_FRa3NZ6VmtXEXhs_nd4KMqt1Y5cWDFxqX7zoJRnAAcEHPXG7eFTzhZn4co9WkLYqSsdMJ9q2Y9k2hF_P56ZLoX63ZgEX_3ofBlv7u10AUF2Z3dzClO3lFraTRkFC1kmU2KBREgJRGgvilNlaNdo7wzKRbh3j0iytr-9vK4z3dK5PzpwUDgw4bIAGgkMgff_j7OuPzyFjNpVAXknsq_O63oJoV997rx0lyZHr7cj15TV06xEaqfoKHAc4lQaOBlVZ3vG_nlRcPEJDV2jyGN0z1RM02j58_RSVf2KJbYF7LHHAEgOWeAdL7LF0LfZY4h5L3GLp7tJjiXssn6GfH2YXp5-iblOMSLn80CbSQLGk4jzOVAF0VVMmTGGoUIYbLlSWGPdjbCrVscqAwnGSwFfHhM65YTFhz9GwspV5gTAzOVWMc80SFk8VgWAfxnMGIULOJXD5MToAy6V-2r5O2-UKJHWGTZ1hx-jtjknTm0V3YY8IRMKSjNEhWDrVpWspMCZwEZJDnJ9IIuNjOkZvegzajrpFyens5NSFsxT47Mu_3OMVerh9ew_QsFmtzSF6oG-asl697t6jW1pEaFM
linkProvider ProQuest Ebooks
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Eigenfunctions+of+transfer+operators+and+automorphic+forms+for+Hecke+triangle+groups+of+infinite+covolume&rft.au=Bruggeman%2C+Roelof+W.&rft.au=Pohl%2C+Anke&rft.date=2023-01-01&rft.pub=American+Mathematical+Society&rft.isbn=9781470465452&rft_id=info:doi/10.1090%2Fmemo%2F1423&rft.externalDocID=BD03747303
thumbnail_m http://cvtisr.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97814704%2F9781470475390.jpg