Explicit formulas for regularized products and series:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1994
|
| Schriftenreihe: | Lecture notes in mathematics
1593 Mathematisches Institut <Bonn>: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn 21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 154 S. |
| ISBN: | 3540586733 |
Internformat
MARC
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| 245 | 1 | 0 | |a Explicit formulas for regularized products and series |c Jay Jorgenson & Serge Lang |
| 249 | |a <<A>> spectral interpretation of Weil's explicit formula |v Dorian Goldfeld | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a VIII, 154 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1593 | |
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| 650 | 4 | |a Functions, Zeta | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Sequences (Mathematics) | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
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| 700 | 1 | 2 | |a Goldfeld, Dorian |d 1947- |0 (DE-588)114451699 |4 aut |t A spectral interpretation of Weil's explicit formula |
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Datensatz im Suchindex
| _version_ | 1805082779645378560 |
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| adam_text |
EXPLICIT FORMULAS FOR REGULARIZED
PRODUCTS AND SERIES
Jay Jorgenson and Serge Lang
Introduction 3
I Asymptotic estimates of regularized harmonic
series 11
1. Regularized products and harmonic series 14
2. Asymptotics in vertical strips 20
3. Asymptotics in sectors 22
4. Asymptotics in a sequence to the left 24
5. Asymptotics in a parallel strip 34
6. Regularized product and series type 36
7. Some examples 39
II Cramer's Theorem as an Explicit Formula 43
1. Euler sums and functional equations 45
2. The general Cramer formula 47
3. Proof of the Cramer theorem 51
4. An inductive theorem 57
III Explicit Formulas under Fourier Assumptions 61
1. Growth conditions on Fourier transforms 62
2. The explicit formulas 66
3. The terms with the q's 73
4. The term involving $ 78
5. The Weil functional and regularized product type 79
IV From Functional Equations to Theta Inversions 85
1. An application of the explicit formulas 87
2. Some examples of theta inversions 92
V From Theta Inversions to Functional Equations 97
1. The Weil functional of a Gaussian test function 99
2. Gauss transforms 101
3. Theta inversions yield zeta functions 109
4. A new zeta function for compact quotients of M3 113
VI A Generalization of Fujii's Theorem 119
1. Statement of the generalized Fujii theorem 122
2. Proof of Fujii's theorem 125
3. Examples 128
Bibliography 131
A SPECTRAL INTERPRETATION OF
WEIL'S EXPLICIT FORMULA
Dorian Goldfeld
1. Introduction 137
2. Notation 139
3. Construction of the indefinite space £2(T) 140
4. Spectral theory of £2(T) 141
5. Eisenstein series 142
6. Cusp forms 145
7. The zeta function associated to an automorphic form
on L2(T) 147
8. The Rankin Selberg convolution 148
9. Higher rank generalizations 148
10. References 152
Index 153 |
| any_adam_object | 1 |
| author | Jorgenson, Jay Lang, Serge 1927-2005 Goldfeld, Dorian 1947- |
| author_GND | (DE-588)119305119 (DE-588)114451699 |
| author_facet | Jorgenson, Jay Lang, Serge 1927-2005 Goldfeld, Dorian 1947- |
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| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV009878687 |
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| indexdate | 2024-07-20T07:38:05Z |
| institution | BVB |
| isbn | 3540586733 |
| language | English |
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| physical | VIII, 154 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| series | Lecture notes in mathematics Mathematisches Institut <Bonn>: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn |
| series2 | Lecture notes in mathematics Mathematisches Institut <Bonn>: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn |
| spelling | Jorgenson, Jay Verfasser aut Explicit formulas for regularized products and series Jay Jorgenson & Serge Lang <<A>> spectral interpretation of Weil's explicit formula Dorian Goldfeld Berlin [u.a.] Springer 1994 VIII, 154 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1593 Mathematisches Institut <Bonn>: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn 21 Expansies (wiskunde) gtt Fonctions zêta L-functies gtt Nombres, Théorie des Spectre (Mathématiques) Suites (Mathématiques) Zeta-functies gtt Functions, Zeta Number theory Sequences (Mathematics) Spectral theory (Mathematics) Regularisierte Reihe (DE-588)4332335-2 gnd rswk-swf Regularisiertes Produkt (DE-588)4332336-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Regularisierte Reihe (DE-588)4332335-2 s Regularisiertes Produkt (DE-588)4332336-4 s Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Goldfeld, Dorian 1947- (DE-588)114451699 aut A spectral interpretation of Weil's explicit formula Lecture notes in mathematics 1593 (DE-604)BV000676446 1593 Mathematisches Institut <Bonn>: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn 21 (DE-604)BV005628488 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006543231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jorgenson, Jay Lang, Serge 1927-2005 Goldfeld, Dorian 1947- Explicit formulas for regularized products and series Lecture notes in mathematics Mathematisches Institut <Bonn>: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn Expansies (wiskunde) gtt Fonctions zêta L-functies gtt Nombres, Théorie des Spectre (Mathématiques) Suites (Mathématiques) Zeta-functies gtt Functions, Zeta Number theory Sequences (Mathematics) Spectral theory (Mathematics) Regularisierte Reihe (DE-588)4332335-2 gnd Regularisiertes Produkt (DE-588)4332336-4 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4332335-2 (DE-588)4332336-4 (DE-588)4067277-3 |
| title | Explicit formulas for regularized products and series |
| title_alt | A spectral interpretation of Weil's explicit formula |
| title_auth | Explicit formulas for regularized products and series |
| title_exact_search | Explicit formulas for regularized products and series |
| title_full | Explicit formulas for regularized products and series Jay Jorgenson & Serge Lang |
| title_fullStr | Explicit formulas for regularized products and series Jay Jorgenson & Serge Lang |
| title_full_unstemmed | Explicit formulas for regularized products and series Jay Jorgenson & Serge Lang |
| title_short | Explicit formulas for regularized products and series |
| title_sort | explicit formulas for regularized products and series |
| topic | Expansies (wiskunde) gtt Fonctions zêta L-functies gtt Nombres, Théorie des Spectre (Mathématiques) Suites (Mathématiques) Zeta-functies gtt Functions, Zeta Number theory Sequences (Mathematics) Spectral theory (Mathematics) Regularisierte Reihe (DE-588)4332335-2 gnd Regularisiertes Produkt (DE-588)4332336-4 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Expansies (wiskunde) Fonctions zêta L-functies Nombres, Théorie des Spectre (Mathématiques) Suites (Mathématiques) Zeta-functies Functions, Zeta Number theory Sequences (Mathematics) Spectral theory (Mathematics) Regularisierte Reihe Regularisiertes Produkt Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006543231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 (DE-604)BV005628488 |
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