Introduction to modular forms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2001
|
| Ausgabe: | 3. print. |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
222 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | IX, 261 S. |
| ISBN: | 3540078339 0387078339 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804133555370983424 |
|---|---|
| adam_text | SERGE LANG INTRODUCTION TO MODULAR FORMS WITH 9 FIGURES SPRINGER TABLE
OF CONTENTS PART I. CLASSICAL THEORY CHAPTER I. MODULAR FORMS 3 § 1. THE
MODULAR GROUP 3 § 2. MODULAR FORMS 5 §3. THE MODULAR FUNCTIONY 12 § 4.
ESTIMATES FOR CUSP FORMS 12 § 5. THE MEILIN TRANSFORM 14 CHAPTER II.
HECKE OPERATORS 16 § 1. DEFINITIONS AND BASIC RELATIONS 16 § 2. EULER
PRODUCTS 21 CHAPTER III. PETERSSON SCALAR PRODUCT 24 § 1. THE RIEMANN
SURFACE T §* 24 § 2. CONGRUENCE SUBGROUPS 29 § 3. DIFFERENTIAL FORMS AND
MODULAR FORMS 32 §4. THE PETERSSON SCALAR PRODUCT 35 APPENDIX BY D.
ZAGIER. THE EICHLER-SELBERG TRACE FORMULA ON SL 2 (Z) . . 44 PART II.
PERIODS OF CUSP FORMS CHAPTER IV. MODULAR SYMBOLS 57 § 1. BASIC
PROPERTIES 57 §2. THE MANIN-DRINFELD THEOREM 61 § 3. HECKE OPERATORS AND
DISTRIBUTIONS 65 CHAPTER V. COEFFICIENTS AND PERIODS OF CUSP FORMS ON 5L
2 (Z) 68 § 1. THE PERIODS AND THEIR INTEGRAL RELATIONS 69 § 2. THE MANIN
RELATIONS 73 VLLL TABLE OF CONTENTS §3. ACTION OFTHE HECKE OPERATORS
ONTHE PERIODS 76 § 4. THE HOMOGENEITY THEOREM 81 CHAPTER VI. THE
EICHLER-SHIMURA ISOMORPHISM ON SL 2 (Z) 84 § 1. THE POLYNOMIAL
REPRESENTATION 85 § 2. THE SHIMURA PRODUCT ON DIFFERENTIAL FORMS 88 §3.
THE IMAGE OFTHE PERIOD MAPPING 89 § 4. COMPUTATION OF DIMENSIONS 93 § 5.
THE MAP INTO COHOMOLOGY 96 PART III. MODULAR FORMS FOR CONGRUENCE
SUBGROUPS CHAPTER VII. HIGHER LEVELS. 101 § 1. THE MODULAR SET AND
MODULAR FORMS 101 § 2. HECKE OPERATORS 105 § 3. HECKE OPERATORS ON § 4.
THE MATRIX OPERATION 111 §5. PETERSSON PRODUCT 112 §6. THE INVOLUTION
114 CHAPTER VIII. ATKIN-LEHNER THEORY 118 §1. CHANGING LEVELS 118 §2.
CHARACTERIZATION OF PRIMITIVE FORMS 122 § 3. THE STRUCTURE THEOREM 123
§4. PROOF OFTHE MAIN THEOREM 126 CHAPTER IX. THE DEDEKIND FORMALISM 138
§ 1. THE TRANSFORMATION FORMALISM 138 §2. EVALUATION OF THE DEDEKIND
SYMBOL 142 PART IV. CONGRUENCE PROPERTIES AND GALOIS REPRESENTATIONS
CHAPTER X. CONGRUENCES AND REDUCTIORI MOD P 151 §1. KUMMER CONGRUENCES
151 §2. VON STAUDT CONGRUENCES 153 § 3. ^-EXPANSIONS 154 § 4. MODULAR
FORMS OVER Z[, |] 156 §5. DERIVATIVES OF MODULAR FORMS 159 §6.
REDUCTIONMODP 162 §7. MODULAR FORMS MOD P,P 5 164 §8. THE OPERATION
OFOEONM 169 TABLEOF CONTENTS IX CHAPTER XI. GALOIS REPRESENTATIONS 176 §
1. SIMPLICITY 177 §2. SUBGROUPSOFGL 2 180 §3. APPLICATIONS TO
CONGRUENCES OF THE TRACE OF FROBENIUS 187 APPENDIX BY WALTER FEIT.
EXCEPTIONAL SUBGROUPS OF GL 2 198 PART V. P-ADIC DISTRIBUTIONS CHAPTER
XII. GENERAL DISTRIBUTIONS 207 § 1. DEFINITIONS 207 § 2. AVERAGING
OPERATORS 210 § 3. THE IWASAWA ALGEBRA 217 § 4. WEIERSTRASS PREPARATION
THEOREM 219 § 5. MODULES OVER Z P [[7]] 221 CHAPTER XIII. BERNOULLI
NUMBERS AND POLYNOMIALS 228 § 1. BERNOULLI NUMBERS AND POLYNOMIALS 228 §
2. THE INTEGRAL DISTRIBUTION 233 § 3. L-FUNCTIONS AND BERNOULLI NUMBERS
236 CHAPTER XIV. THE COMPLEX L-FUNCTIONS 240 §1. THE HURWITZ ZETA
FUNCTION 240 § 2. FUNCTIONAL EQUATION 244 CHAPTER XV. THE
HECKE-EISENSTEIN AND KLEIN FORMS 247 §1. FORMS OFWEIGHT 1 247 § 2. THE
KLEIN FORMS 251 §3. FORMS OFWEIGHT 2 252 BIBLIOGRAPHY . . . 255 SUBJECT
INDEX 260
|
| any_adam_object | 1 |
| author | Lang, Serge 1927-2005 |
| author_GND | (DE-588)119305119 |
| author_facet | Lang, Serge 1927-2005 |
| author_role | aut |
| author_sort | Lang, Serge 1927-2005 |
| author_variant | s l sl |
| building | Verbundindex |
| bvnumber | BV020003266 |
| classification_rvk | SK 180 SK 750 |
| ctrlnum | (OCoLC)265455331 (DE-599)BVBBV020003266 |
| discipline | Mathematik |
| edition | 3. print. |
| format | Book |
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| id | DE-604.BV020003266 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:10:35Z |
| institution | BVB |
| isbn | 3540078339 0387078339 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013324952 |
| oclc_num | 265455331 |
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| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | IX, 261 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Introduction to modular forms Serge Lang 3. print. Berlin [u.a.] Springer 2001 IX, 261 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 222 Literaturangaben Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Modulform (DE-588)4128299-1 s DE-604 Algebraische Zahlentheorie (DE-588)4001170-7 s Automorphe Form (DE-588)4003972-9 s 1\p DE-604 Funktionentheorie (DE-588)4018935-1 s 2\p DE-604 Grundlehren der mathematischen Wissenschaften 222 (DE-604)BV000000395 222 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013324952&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge 1927-2005 Introduction to modular forms Grundlehren der mathematischen Wissenschaften Algebraische Zahlentheorie (DE-588)4001170-7 gnd Modulform (DE-588)4128299-1 gnd Automorphe Form (DE-588)4003972-9 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4128299-1 (DE-588)4003972-9 (DE-588)4018935-1 |
| title | Introduction to modular forms |
| title_auth | Introduction to modular forms |
| title_exact_search | Introduction to modular forms |
| title_full | Introduction to modular forms Serge Lang |
| title_fullStr | Introduction to modular forms Serge Lang |
| title_full_unstemmed | Introduction to modular forms Serge Lang |
| title_short | Introduction to modular forms |
| title_sort | introduction to modular forms |
| topic | Algebraische Zahlentheorie (DE-588)4001170-7 gnd Modulform (DE-588)4128299-1 gnd Automorphe Form (DE-588)4003972-9 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Algebraische Zahlentheorie Modulform Automorphe Form Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013324952&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT langserge introductiontomodularforms |