Non-vanishing of L-functions and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1997
|
| Series: | Progress in mathematics
157 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | X, 196 S. Ill. |
| ISBN: | 3764358017 0817658017 |
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MARC
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| 245 | 1 | 0 | |a Non-vanishing of L-functions and applications |c M. Ram Murty ; V. Kumar Murty |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1997 | |
| 300 | |a X, 196 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 157 | |
| 500 | |a Literaturangaben | ||
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| 650 | 7 | |a Equidistribution |2 Jussieu | |
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| 650 | 7 | |a Fonctions l |2 ram | |
| 650 | 7 | |a L-functies |2 gtt | |
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| 650 | 7 | |a Répartition nombre entier |2 Jussieu | |
| 650 | 4 | |a L-functions | |
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Record in the Search Index
| _version_ | 1804126037826600960 |
|---|---|
| adam_text | Table of Contents
Preface xi
Introduction 1
Chapter 1 The Prime Number Theorem and Generalizations
§ 1 The Prime Number Theorem 5
§ 2 Primes in arithmetic progressions 15
§ 3 Dedekind s zeta function 19
§ 4 Hecke L functions 21
Chapter 2 Artin L functions
§ 1 Group theoretic background 25
§ 2 Definition and basic properties of Artin L functions 27
§ 3 The Aramata Brauer theorem 30
§ 4 Dedekind s conjecture in the non Galois case 32
§ 5 Zeros and poles of Artin L functions 35
§ 6 Low order zeros of Dedekind zeta functions 37
§ 7 The Chebotarev Density Theorem 41
§ 8 Consequences of Artin s conjecture 46
§ 9 The least prime in a conjugacy class 52
Chapter 3 Equidistribution and L functions
§ 1 Compact groups and Haar measures 65
§ 2 Weyl s criterion for equidistribution 66
§ 3 L functions on G 67
§ 4 Deligne s prime number theorem 68
x Table of Contents
Chapter 4 Modular Forms and Dirichlet Series
§ 1 SLi(J^) and some of its subgroups 75
§ 2 The upper half plane 76
§ 3 Modular forms and cusp forms 77
§ 4 L functions and Hecke s theorem 81
§ 5 Hecke operators 82
§ 6 Oldforms and Newforms 83
§ 7 The Sato Tate conjecture 83
§ 8 Oscillations of Fourier coefficients of newforms 84
§ 9 Rankin s theorem 90
Chapter 5 Dirichlet L functions
§ 1 Average value of L(s, x) 93
§ 2 Polya Vinogradov estimate 95
§ 3 Jutila s character sum estimate 97
§ 4 Average value of L(~, d) 104
§ 5 Non vanishing for a positive proportion of characters, I 110
§ 6 Non vanishing for a positive proportion of characters, II 119
§ 7 A conditional improvement 128
Chapter 6 Non vanishing of Quadratic Twists of Modular L functions
§ 1 Introduction 133
§ 2 The integrated Polya Vinogradov estimate 141
§ 3 The main terms 142
§ 4 Estimates for real character sums 152
§ 5 Estimates for some weighted sums 158
§6 The statements A±(a) and C±(a) 160
§ 7 Proof of main result 170
Chapter 7 Selberg s Conjectures
§ 1 Selberg s class of Dirichlet series 177
§ 2 Basic consequences 180
§ 3 Artin s conjecture and Selberg s conjectures 181
Chapter 8 Suggestions for further reading 187
Author Index 192
Subject Index 194
|
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.73 |
| dewey-sort | 3512 273 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV011515552 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:05Z |
| institution | BVB |
| isbn | 3764358017 0817658017 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007750425 |
| oclc_num | 37579795 |
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| physical | X, 196 S. Ill. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Murty, Maruti Ram 1953- Verfasser (DE-588)120837307 aut Non-vanishing of L-functions and applications M. Ram Murty ; V. Kumar Murty Basel [u.a.] Birkhäuser 1997 X, 196 S. Ill. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 157 Literaturangaben Biographie Balaguer Jussieu Conjecture Selberg Jussieu Equidistribution Jussieu Fonction L Artin Jussieu Fonctions l ram L-functies gtt Portrait Balaguer Jussieu Répartition nombre entier Jussieu L-functions L-Funktion (DE-588)4137026-0 gnd rswk-swf L-Funktion (DE-588)4137026-0 s DE-604 Murty, Vijaya Kumar 1956- Verfasser (DE-588)104255765 aut Progress in mathematics 157 (DE-604)BV000004120 157 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007750425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Murty, Maruti Ram 1953- Murty, Vijaya Kumar 1956- Non-vanishing of L-functions and applications Progress in mathematics Biographie Balaguer Jussieu Conjecture Selberg Jussieu Equidistribution Jussieu Fonction L Artin Jussieu Fonctions l ram L-functies gtt Portrait Balaguer Jussieu Répartition nombre entier Jussieu L-functions L-Funktion (DE-588)4137026-0 gnd |
| subject_GND | (DE-588)4137026-0 |
| title | Non-vanishing of L-functions and applications |
| title_auth | Non-vanishing of L-functions and applications |
| title_exact_search | Non-vanishing of L-functions and applications |
| title_full | Non-vanishing of L-functions and applications M. Ram Murty ; V. Kumar Murty |
| title_fullStr | Non-vanishing of L-functions and applications M. Ram Murty ; V. Kumar Murty |
| title_full_unstemmed | Non-vanishing of L-functions and applications M. Ram Murty ; V. Kumar Murty |
| title_short | Non-vanishing of L-functions and applications |
| title_sort | non vanishing of l functions and applications |
| topic | Biographie Balaguer Jussieu Conjecture Selberg Jussieu Equidistribution Jussieu Fonction L Artin Jussieu Fonctions l ram L-functies gtt Portrait Balaguer Jussieu Répartition nombre entier Jussieu L-functions L-Funktion (DE-588)4137026-0 gnd |
| topic_facet | Biographie Balaguer Conjecture Selberg Equidistribution Fonction L Artin Fonctions l L-functies Portrait Balaguer Répartition nombre entier L-functions L-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007750425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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