Complex multiplication:
"This is a self-contained account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of ellip...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | New mathematical monographs
15 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This is a self-contained account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. The main results are accompanied by numerical examples, equipping any reader with all the tools and formulas they need. Topics covered include: the construction of class fields over quadratic imaginary number fields by singular values of the modular invariant j and Weber's tau-function; explicit construction of rings of integers in ray class fields and Galois module structure; the construction of cryptographically relevant elliptic curves over finite fields; proof of Berwick's congruences using division values of the Weierstrass p-function; relations between elliptic units and class numbers"--Provided by publisher. |
| Beschreibung: | Literaturverz. S. 351 - 355 |
| Beschreibung: | XIII, 361 S. |
| ISBN: | 9780521766685 |
Internformat
MARC
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| 650 | 4 | |a Multiplication, Complex | |
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Datensatz im Suchindex
| _version_ | 1804141165634650112 |
|---|---|
| adam_text | COMPLEX MULTIPLICATION
/ SCHERTZ, REINHARD
: 2010
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE; 1. ELLIPTIC FUNCTIONS; 2. MODULAR FUNCTIONS; 3. BASIC FACTS
FROM NUMBER THEORY; 4. FACTORISATION OF SINGULAR VALUES; 5. THE
RECIPROCITY LAW; 6. GENERATION OF RING CLASS FIELDS AND RAY CLASS
FIELDS; 7. INTEGRAL BASIS IN RAY CLASS FIELDS; 8. GALOIS MODULE
STRUCTURE; 9. BERWICK S CONGRUENCES; 10. CRYPTOGRAPHICALLY RELEVANT
ELLIPTIC CURVES; 11. THE CLASS NUMBER FORMULAS OF CURT MEYER; 12.
ARITHMETIC INTERPRETATION OF CLASS NUMBER FORMULAS; REFERENCES; INDEX OF
NOTATION; INDEX.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Schertz, Reinhard 1943- |
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| 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 | 1. publ. |
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| id | DE-604.BV036098237 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:32Z |
| institution | BVB |
| isbn | 9780521766685 |
| language | English |
| lccn | 2009051874 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018988674 |
| oclc_num | 449827362 |
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| physical | XIII, 361 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | New mathematical monographs |
| series2 | New mathematical monographs |
| spelling | Schertz, Reinhard 1943- Verfasser (DE-588)117723789 aut Complex multiplication Reinhard Schertz 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XIII, 361 S. txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 15 Literaturverz. S. 351 - 355 "This is a self-contained account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. The main results are accompanied by numerical examples, equipping any reader with all the tools and formulas they need. Topics covered include: the construction of class fields over quadratic imaginary number fields by singular values of the modular invariant j and Weber's tau-function; explicit construction of rings of integers in ray class fields and Galois module structure; the construction of cryptographically relevant elliptic curves over finite fields; proof of Berwick's congruences using division values of the Weierstrass p-function; relations between elliptic units and class numbers"--Provided by publisher. Multiplication, Complex Komplexe Multiplikation (DE-588)4164903-5 gnd rswk-swf Modulfunktion (DE-588)4039855-9 gnd rswk-swf Elliptische Funktion (DE-588)4134665-8 gnd rswk-swf Komplexe Multiplikation (DE-588)4164903-5 s Elliptische Funktion (DE-588)4134665-8 s Modulfunktion (DE-588)4039855-9 s DE-604 New mathematical monographs 15 (DE-604)BV035420183 15 LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018988674&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schertz, Reinhard 1943- Complex multiplication New mathematical monographs Multiplication, Complex Komplexe Multiplikation (DE-588)4164903-5 gnd Modulfunktion (DE-588)4039855-9 gnd Elliptische Funktion (DE-588)4134665-8 gnd |
| subject_GND | (DE-588)4164903-5 (DE-588)4039855-9 (DE-588)4134665-8 |
| title | Complex multiplication |
| title_auth | Complex multiplication |
| title_exact_search | Complex multiplication |
| title_full | Complex multiplication Reinhard Schertz |
| title_fullStr | Complex multiplication Reinhard Schertz |
| title_full_unstemmed | Complex multiplication Reinhard Schertz |
| title_short | Complex multiplication |
| title_sort | complex multiplication |
| topic | Multiplication, Complex Komplexe Multiplikation (DE-588)4164903-5 gnd Modulfunktion (DE-588)4039855-9 gnd Elliptische Funktion (DE-588)4134665-8 gnd |
| topic_facet | Multiplication, Complex Komplexe Multiplikation Modulfunktion Elliptische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018988674&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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