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Complex multiplication /

Schertz, Reinhard, (1943-)

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Complex multiplication /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Complex multiplication // Reinhard Schertz.
作者:	Schertz, Reinhard,
出版者:	Cambridge, UK ;Cambridge University Press, : 2010.,
面頁冊數:	xiii, 361 p. :ill. ;24 cm.
內容註:	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.
標題:	Multiplication, Complex. -
電子資源:	http://assets.cambridge.org/97805217/66685/cover/9780521766685.jpg
電子資源:	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 /
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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