Elementary Dirichlet series and modular forms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2007
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 147 S. |
| ISBN: | 9780387724737 9780387724744 |
Internformat
MARC
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| 100 | 1 | |a Shimura, Goro |d 1930-2019 |e Verfasser |0 (DE-588)12425067X |4 aut | |
| 245 | 1 | 0 | |a Elementary Dirichlet series and modular forms |c Goro Shimura |
| 264 | 1 | |a New York, NY |b Springer |c 2007 | |
| 300 | |a VIII, 147 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804137228736135168 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
Preface
v
Introduction
1
Chapter I. Preliminaries on Modular Forms and
Dirichlet Series
5
1.
Basic symbols and the definition of modular forma
5
2.
Elementary Fourier analysis
13
3.
The functional equation of a Dirichlet series
19
Chapter II. Critical Values of Dirichlet L-functions
25
4.
The values of elementary Dirichlet series at integers
25
5.
The class number of a cyclotomic field
39
6.
Some more formulas for L(k,
χ)
45
Chapter III. The Case of Imaginary Quadratic Fields
and Nearly Holomorphic Modular Forms
53
7.
Dirichlet series associated with an imaginary quadratic
field
53
8.
Nearly holomorphic modular forms
55
Chapter IV.
Eisenstein
Series
59
9.
Fourier expansion of
Eisenstein
series
59
10.
Polynomial relations between
Eisenstein
series
66
11.
Recurrence formulas for the critical values of certain
Dirichlet series
75
Chapter V. Critical Values of Dirichlet Series Asso¬
ciated with Imaginary Quadratic Fields
79
12.
The singular values of nearly holomorphic forms
79
13.
The critical values of L-functions of an imaginary qua¬
dratic field
84
14.
The
zeta
function of a member of a one-parameter fam¬
ily of elliptic curves
96
Chapter VI. Supplementary Results
113
15.
Isomorphism classes of abelian varieties with complex
multiplication
113
15А.
The general case
113
15B. The case of elliptic curves
117
16.
Holomorphic differential operators on the upper half
plane
120
Appendix
127
Al.
Integration and differentiation under the integral sign
127
A2. Fourier series with parameters
130
A3.
The confluent hypergeometric function
131
A4.
The
Weierstrass p-function
136
A5. The action of Ga+ on modular forms
139
References
145
Index
147
|
| adam_txt |
TABLE
OF
CONTENTS
Preface
v
Introduction
1
Chapter I. Preliminaries on Modular Forms and
Dirichlet Series
5
1.
Basic symbols and the definition of modular forma
5
2.
Elementary Fourier analysis
13
3.
The functional equation of a Dirichlet series
19
Chapter II. Critical Values of Dirichlet L-functions
25
4.
The values of elementary Dirichlet series at integers
25
5.
The class number of a cyclotomic field
39
6.
Some more formulas for L(k,
χ)
45
Chapter III. The Case of Imaginary Quadratic Fields
and Nearly Holomorphic Modular Forms
53
7.
Dirichlet series associated with an imaginary quadratic
field
53
8.
Nearly holomorphic modular forms
55
Chapter IV.
Eisenstein
Series
59
9.
Fourier expansion of
Eisenstein
series
59
10.
Polynomial relations between
Eisenstein
series
66
11.
Recurrence formulas for the critical values of certain
Dirichlet series
75
Chapter V. Critical Values of Dirichlet Series Asso¬
ciated with Imaginary Quadratic Fields
79
12.
The singular values of nearly holomorphic forms
79
13.
The critical values of L-functions of an imaginary qua¬
dratic field
84
14.
The
zeta
function of a member of a one-parameter fam¬
ily of elliptic curves
96
Chapter VI. Supplementary Results
113
15.
Isomorphism classes of abelian varieties with complex
multiplication
113
15А.
The general case
113
15B. The case of elliptic curves
117
16.
Holomorphic differential operators on the upper half
plane
120
Appendix
127
Al.
Integration and differentiation under the integral sign
127
A2. Fourier series with parameters
130
A3.
The confluent hypergeometric function
131
A4.
The
Weierstrass p-function
136
A5. The action of Ga+ on modular forms
139
References
145
Index
147 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:10:16Z |
| indexdate | 2024-07-09T21:08:58Z |
| institution | BVB |
| isbn | 9780387724737 9780387724744 |
| language | English |
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| physical | VIII, 147 S. |
| publishDate | 2007 |
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| spelling | Shimura, Goro 1930-2019 Verfasser (DE-588)12425067X aut Elementary Dirichlet series and modular forms Goro Shimura New York, NY Springer 2007 VIII, 147 S. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Dirichlet series Forms, Modular L-functions Dirichlet-Reihe (DE-588)4150139-1 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Dirichlet-Reihe (DE-588)4150139-1 s Modulform (DE-588)4128299-1 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016217425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shimura, Goro 1930-2019 Elementary Dirichlet series and modular forms Dirichlet series Forms, Modular L-functions Dirichlet-Reihe (DE-588)4150139-1 gnd Modulform (DE-588)4128299-1 gnd |
| subject_GND | (DE-588)4150139-1 (DE-588)4128299-1 |
| title | Elementary Dirichlet series and modular forms |
| title_auth | Elementary Dirichlet series and modular forms |
| title_exact_search | Elementary Dirichlet series and modular forms |
| title_exact_search_txtP | Elementary Dirichlet series and modular forms |
| title_full | Elementary Dirichlet series and modular forms Goro Shimura |
| title_fullStr | Elementary Dirichlet series and modular forms Goro Shimura |
| title_full_unstemmed | Elementary Dirichlet series and modular forms Goro Shimura |
| title_short | Elementary Dirichlet series and modular forms |
| title_sort | elementary dirichlet series and modular forms |
| topic | Dirichlet series Forms, Modular L-functions Dirichlet-Reihe (DE-588)4150139-1 gnd Modulform (DE-588)4128299-1 gnd |
| topic_facet | Dirichlet series Forms, Modular L-functions Dirichlet-Reihe Modulform |
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