Modular functions in analytic number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chicago
Markham
1970
|
| Schriftenreihe: | Markham mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 150 S. |
| ISBN: | 0841010005 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804116906331865088 |
|---|---|
| adam_text | CONTENTS
PREFACE vii
Chapter 1 THE MODULAR GROUP AND
CERTAIN SUBGROUPS
1 The Modular Group 1
2 A Fundamental Region for T(l) 3
3 Some Subgroups of F(l) 5
4 Fundamental Regions of Subgroups 9
Chapter 2 MODULAR FUNCTIONS AND FORMS
1 Multiplier Systems 12
2 Parabolic Points 13
3 Fourier Expansions 17
4 Definitions of Modular Function and Modular
Form 23
5 Several Important Theorems 24
Chapter 3 THE MODULAR FORMS n{x) AND 9{t)
1 The Function n(i) 32
2 Several Famous Identities 34
3 Transformation Formulas for ^(t) 39
4 The Function %) 45
Chapter 4 THE MULTIPLIER SYSTEMS v, AND vA
1 Preliminaries 49
ix
X CONTENTS
2 Proof of Theorem 2 51
3 Proof of Theorem 3 60
Chapter 5 SUMS OF SQUARES
1 Statement of Results 63
2 Lipschitz Summation Formula 65
3 The Function ps{z) 72
4 The Expansion of tj/s(z) at 1 75
5 Proofs of Theorems 2 and 3 80
6 Related Results 81
Chapter 6 THE ORDER OF MAGNITUDE
OF p(n)
1 A Simple Inequality for p(n) 88
2 The Asymptotic Formula for p(n) 90
3 Proof of Theorem 2 93
Chapter 7 THE RAMANUJAN CONGRUENCES
FOR p(n)
1 Statement of the Congruences 100
2 The Functions J p,,.(t) and hp(x) 101
3 The Function sp r(T.) 105
4 The Congruence for p(n) Modulo 11 116
5 Newton s Formula 118
6 The Modular Equation for the Prime 5 119
7 The Modular Equation for the Prime 7 121
Chapter 8 PROOF OF THE RAMANUJAN
CONGRUENCES FOR POWERS
OF 5 AND 7
1 Preliminaries 124
2 Application of the Modular Equation 128
3 A Digression: The Ramanujan Identities for Powers
of the Prime 5 131
4 Completion of the Proof for Powers of 5 134
5 Start of the Proof for Powers of 7 137
6 A Second Digression: The Ramanujan Identities for
Powers of the Prime 7 142
7 Completion of the Proof for Powers of 7 143
INDEX 149
|
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| author | Knopp, Marvin Isadore 1933- |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.81 |
| dewey-search | 512/.81 |
| dewey-sort | 3512 281 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002499969 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:45:57Z |
| institution | BVB |
| isbn | 0841010005 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001610441 |
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| publisher | Markham |
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| spelling | Knopp, Marvin Isadore 1933- Verfasser (DE-588)115373225 aut Modular functions in analytic number theory Chicago Markham 1970 X, 150 S. txt rdacontent n rdamedia nc rdacarrier Markham mathematics series Fonctions modulaires Nombres, Théorie des Modular functions Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Modulfunktion (DE-588)4039855-9 gnd rswk-swf Modulfunktion (DE-588)4039855-9 s Analytische Zahlentheorie (DE-588)4001870-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001610441&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Knopp, Marvin Isadore 1933- Modular functions in analytic number theory Fonctions modulaires Nombres, Théorie des Modular functions Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd Modulfunktion (DE-588)4039855-9 gnd |
| subject_GND | (DE-588)4001870-2 (DE-588)4039855-9 |
| title | Modular functions in analytic number theory |
| title_auth | Modular functions in analytic number theory |
| title_exact_search | Modular functions in analytic number theory |
| title_full | Modular functions in analytic number theory |
| title_fullStr | Modular functions in analytic number theory |
| title_full_unstemmed | Modular functions in analytic number theory |
| title_short | Modular functions in analytic number theory |
| title_sort | modular functions in analytic number theory |
| topic | Fonctions modulaires Nombres, Théorie des Modular functions Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd Modulfunktion (DE-588)4039855-9 gnd |
| topic_facet | Fonctions modulaires Nombres, Théorie des Modular functions Number theory Analytische Zahlentheorie Modulfunktion |
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