Spectral theory of the Riemann zeta-function:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
127 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | IX, 228 S. |
| ISBN: | 0521445205 9780521445207 9780521058070 |
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MARC
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| 100 | 1 | |a Motohashi, Yoichi |d 1944- |e Verfasser |0 (DE-588)11030764X |4 aut | |
| 245 | 1 | 0 | |a Spectral theory of the Riemann zeta-function |c Yoichi Motohashi |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1997 | |
| 300 | |a IX, 228 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics |v 127 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Fonction zêta Riemann | |
| 650 | 7 | |a Fonctions zeta |2 ram | |
| 650 | 4 | |a Formule trace | |
| 650 | 4 | |a Opérateur Hecke | |
| 650 | 4 | |a Somme Kloosterman | |
| 650 | 7 | |a Spectraaltheorie |2 gtt | |
| 650 | 7 | |a Théorie spectrale |2 ram | |
| 650 | 7 | |a Zeta-functies |2 gtt | |
| 650 | 4 | |a Functions, Zeta | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zetafunktion |0 (DE-588)4190764-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zetafunktion |0 (DE-588)4190764-4 |D s |
| 689 | 0 | 1 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
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| 830 | 0 | |a Cambridge tracts in mathematics |v 127 |w (DE-604)BV000000001 |9 127 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007872424 | |
Record in the Search Index
| _version_ | 1825578090683695104 |
|---|---|
| adam_text |
Contents
Preface page vii
Convention and assumed background viii
1 Non Euclidean harmonics 1
1.1 Basic concepts 1
1.2 Resolvent kernel 17
1.3 Iterated kernel 22
1.4 Spectral resolution 32
1.5 Notes for Chapter 1 40
2 Trace formulas 43
2.1 Basic identities 43
2.2 Holomorphic forms 49
2.3 Spectral means of Maass Fourier coefficients 54
2.4 Sums of Kloosterman sums 61
2.5 Opposite sign case 67
2.6 Alternative argument 72
2.7 A flight 83
2.8 Notes for Chapter 2 90
3 Automorphic /. functions 97
3.1 Hecke operators 97
3.2 L functions 104
3.3 Bilinear forms of L functions 111
3.4 Spectral mean values 121
3.5 Spectral large sieve 131
3.6 Notes for Chapter 3 139
v
vi Contents
4 An explicit formula 144
4.1 A prototype 145
4.2 Non diagonals 150
4.3 Reduction to Kloosterman sums 153
4.4 Spectral expansion 158
4.5 Crystallization 164
4.6 Analytic continuation 166
4.7 Explicit formula 171
4.8 Notes for Chapter 4 178
5 Asymptotics 185
5.1 Local explicit formula 185
5.2 Global bounds 199
5.3 Eigen peaks 205
5.4 Notes for Chapter 5, and epilogue 212
References 221
Author index 225
Subject index 227 |
| any_adam_object | 1 |
| author | Motohashi, Yoichi 1944- |
| author_GND | (DE-588)11030764X |
| author_facet | Motohashi, Yoichi 1944- |
| author_role | aut |
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| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)35638161 (DE-599)BVBBV011677656 |
| dewey-full | 512/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.73 |
| dewey-search | 512/.73 |
| dewey-sort | 3512 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV011677656 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T13:02:17Z |
| institution | BVB |
| isbn | 0521445205 9780521445207 9780521058070 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007872424 |
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| physical | IX, 228 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Motohashi, Yoichi 1944- Verfasser (DE-588)11030764X aut Spectral theory of the Riemann zeta-function Yoichi Motohashi 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1997 IX, 228 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 127 Hier auch später erschienene, unveränderte Nachdrucke Fonction zêta Riemann Fonctions zeta ram Formule trace Opérateur Hecke Somme Kloosterman Spectraaltheorie gtt Théorie spectrale ram Zeta-functies gtt Functions, Zeta Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s Spektraltheorie (DE-588)4116561-5 s DE-604 Cambridge tracts in mathematics 127 (DE-604)BV000000001 127 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007872424&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Motohashi, Yoichi 1944- Spectral theory of the Riemann zeta-function Cambridge tracts in mathematics Fonction zêta Riemann Fonctions zeta ram Formule trace Opérateur Hecke Somme Kloosterman Spectraaltheorie gtt Théorie spectrale ram Zeta-functies gtt Functions, Zeta Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4190764-4 |
| title | Spectral theory of the Riemann zeta-function |
| title_auth | Spectral theory of the Riemann zeta-function |
| title_exact_search | Spectral theory of the Riemann zeta-function |
| title_full | Spectral theory of the Riemann zeta-function Yoichi Motohashi |
| title_fullStr | Spectral theory of the Riemann zeta-function Yoichi Motohashi |
| title_full_unstemmed | Spectral theory of the Riemann zeta-function Yoichi Motohashi |
| title_short | Spectral theory of the Riemann zeta-function |
| title_sort | spectral theory of the riemann zeta function |
| topic | Fonction zêta Riemann Fonctions zeta ram Formule trace Opérateur Hecke Somme Kloosterman Spectraaltheorie gtt Théorie spectrale ram Zeta-functies gtt Functions, Zeta Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Fonction zêta Riemann Fonctions zeta Formule trace Opérateur Hecke Somme Kloosterman Spectraaltheorie Théorie spectrale Zeta-functies Functions, Zeta Spectral theory (Mathematics) Spektraltheorie Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007872424&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT motohashiyoichi spectraltheoryoftheriemannzetafunction |