東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Complex multiplication /

Schertz, Reinhard, (1943-)

Linked to FindBook

Google Book

Amazon

博客來

Complex multiplication /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Complex multiplication // Reinhard Schertz.
Author:	Schertz, Reinhard,
Published:	Cambridge, UK ;Cambridge University Press, : 2010.,
Description:	xiii, 361 p. :ill. ;24 cm.
[NT 15003449]:	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.
Subject:	Multiplication, Complex. -
Online resource:	http://assets.cambridge.org/97805217/66685/cover/9780521766685.jpg
Online resource:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018988674&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
ISBN:	9780521766685 (hardback) :

Complex multiplication /
Schertz, Reinhard,1943-

Complex multiplication /Reinhard Schertz. - Cambridge, UK ;Cambridge University Press,2010. - xiii, 361 p. :ill. ;24 cm. - New mathematical monographs ;15. - New mathematical monographs ;13..

Includes bibliographical references (p. 351-355) and indexes.

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.

"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.

ISBN: 9780521766685 (hardback) :US99.00

LCCN: 2009051874

Nat. Bib. No.: GBB004264bnb

Nat. Bib. Agency Control No.: 015462084UkSubjects--Topical Terms:

940946
Multiplication, Complex.

LC Class. No.: QA564 / .S294 2010

Dewey Class. No.: 516.3/52

Complex multiplication /
LDR:02689cam 2200289 a 4500 001 975124
003 DLC
005 20101101100447.0
008 111017s2010 enka b 001 0 eng
010 $a 2009051874
015 $a GBB004264 $2 bnb
016 7 $a 015462084 $2 Uk
020 $a 9780521766685 (hardback) : $c US99.00
020 $a 0521766680 (hardback)
035 $a (OCoLC)ocn449827362
035 $a AAS-BW-100-N-01
040 $a DLC $b eng $c DLC $d BTCTA $d BWKUK $d BWK $d UKM $d DEBBG $d CDX $d YDXCP $d OCL $d BWX $d OCL $d IUL $d DLC
050 0 0 $a QA564 $b .S294 2010
082 0 0 $a 516.3/52 $2 22
100 1 $a Schertz, Reinhard, $d 1943- $3 1299037
245 1 0 $a Complex multiplication / $c Reinhard Schertz.
260 # $a Cambridge, UK ; $a New York : $b Cambridge University Press, $c 2010.
300 $a xiii, 361 p. : $b ill. ; $c 24 cm.
490 1 $a New mathematical monographs ; $v 15
504 $a Includes bibliographical references (p. 351-355) and indexes.
505 0 # $a 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.
520 # $a "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.
650 # 0 $a Multiplication, Complex. $3 940946
830 0 $a New mathematical monographs ; $v 13. $3 1232924
856 4 2 $3 Cover image $u http://assets.cambridge.org/97805217/66685/cover/9780521766685.jpg
856 4 1 $3 Table of contents $u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018988674&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA