Introduction to elliptic curves and modular forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1993
|
| Edition: | 2. ed. |
| Series: | Graduate texts in mathematics
97 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | X, 248 S. Ill., graph. Darst. |
| ISBN: | 0387979662 3540979662 |
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| 100 | 1 | |a Koblitz, Neal |d 1948- |e Verfasser |0 (DE-588)108974820 |4 aut | |
| 245 | 1 | 0 | |a Introduction to elliptic curves and modular forms |c Neal Koblitz |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1993 | |
| 300 | |a X, 248 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 97 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 650 | 4 | |a Formes modulaires | |
| 650 | 7 | |a Formes modulaires |2 ram | |
| 650 | 4 | |a Nombres, Théorie des | |
| 650 | 7 | |a Nombres, théorie des |2 ram | |
| 650 | 7 | |a Teoria dos números |2 larpcal | |
| 650 | 4 | |a Curves, Elliptic | |
| 650 | 4 | |a Forms, Modular | |
| 650 | 4 | |a Number theory | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface to the First Edition v
Preface to the Second Edition vii
CHAPTER I
From Congruent Numbers to Elliptic Curves 1
1. Congruent numbers 3
2. A certain cubic equation 6
3. Elliptic curves 9
4. Doubly periodic functions 14
5. The field of elliptic functions 18
6. Elliptic curves in Weierstrass form 22
7. The addition law 29
8. Points of finite order 36
9. Points over finite fields, and the congruent number problem 43
CHAPTER II
The Hasse Weil /. Function of an Elliptic Curve 51
1. The congruence zeta function 51
2. The zeta function of En 56
3. Varying the prime/? 64
4. The prototype: the Riemann zeta function 70
5. The Hasse Weil /. function and its functional equation 79
6. The critical value 90
X Contents
CHAPTER III
Modular forms 98
1. SL2(T) and its congruence subgroups 98
2. Modular forms for SL2(Z) 108
3. Modular forms for congruence subgroups 124
4. Transformation formula for the theta function 147
5. The modular interpretation, and Hecke operators 153
CHAPTER IV
Modular Forms of Half Integer Weight 176
1. Definitions and examples 177
2. Eisenstein series of half integer weight for Fo(4) 185
3. Hecke operators on forms of half integer weight 202
4. The theorems of Shimura, Waldspurger, Tunnell, and the congruent
number problem 212
Answers, Hints, and References for Selected Exercises 223
Bibliography 240
Index 245
|
| any_adam_object | 1 |
| author | Koblitz, Neal 1948- |
| author_GND | (DE-588)108974820 |
| author_facet | Koblitz, Neal 1948- |
| author_role | aut |
| author_sort | Koblitz, Neal 1948- |
| author_variant | n k nk |
| building | Verbundindex |
| bvnumber | BV007741846 |
| callnumber-first | Q - Science |
| callnumber-label | QA567 |
| callnumber-raw | QA567.2.E44 |
| callnumber-search | QA567.2.E44 |
| callnumber-sort | QA 3567.2 E44 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 240 |
| classification_tum | MAT 145f MAT 103f |
| ctrlnum | (OCoLC)27070721 (DE-599)BVBBV007741846 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV007741846 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:08:43Z |
| institution | BVB |
| isbn | 0387979662 3540979662 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005090001 |
| oclc_num | 27070721 |
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| physical | X, 248 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Koblitz, Neal 1948- Verfasser (DE-588)108974820 aut Introduction to elliptic curves and modular forms Neal Koblitz 2. ed. New York [u.a.] Springer 1993 X, 248 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 97 Hier auch später erschienene, unveränderte Nachdrucke Courbes elliptiques Courbes elliptiques ram Curvas eliticas larpcal Formes modulaires Formes modulaires ram Nombres, Théorie des Nombres, théorie des ram Teoria dos números larpcal Curves, Elliptic Forms, Modular Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Modulform (DE-588)4128299-1 s DE-604 Zahlentheorie (DE-588)4067277-3 s Graduate texts in mathematics 97 (DE-604)BV000000067 97 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005090001&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koblitz, Neal 1948- Introduction to elliptic curves and modular forms Graduate texts in mathematics Courbes elliptiques Courbes elliptiques ram Curvas eliticas larpcal Formes modulaires Formes modulaires ram Nombres, Théorie des Nombres, théorie des ram Teoria dos números larpcal Curves, Elliptic Forms, Modular Number theory Zahlentheorie (DE-588)4067277-3 gnd Modulform (DE-588)4128299-1 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4128299-1 (DE-588)4014487-2 |
| title | Introduction to elliptic curves and modular forms |
| title_auth | Introduction to elliptic curves and modular forms |
| title_exact_search | Introduction to elliptic curves and modular forms |
| title_full | Introduction to elliptic curves and modular forms Neal Koblitz |
| title_fullStr | Introduction to elliptic curves and modular forms Neal Koblitz |
| title_full_unstemmed | Introduction to elliptic curves and modular forms Neal Koblitz |
| title_short | Introduction to elliptic curves and modular forms |
| title_sort | introduction to elliptic curves and modular forms |
| topic | Courbes elliptiques Courbes elliptiques ram Curvas eliticas larpcal Formes modulaires Formes modulaires ram Nombres, Théorie des Nombres, théorie des ram Teoria dos números larpcal Curves, Elliptic Forms, Modular Number theory Zahlentheorie (DE-588)4067277-3 gnd Modulform (DE-588)4128299-1 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| topic_facet | Courbes elliptiques Curvas eliticas Formes modulaires Nombres, Théorie des Nombres, théorie des Teoria dos números Curves, Elliptic Forms, Modular Number theory Zahlentheorie Modulform Elliptische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005090001&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT koblitzneal introductiontoellipticcurvesandmodularforms |