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010 a| 2009051874;

015 a| GBB0042642| bnb;

016 7 a| 0154620842| Uk;

020 a| 9780521766685 (hardback);

035 a| (WaSeSS)ssj0000399879;

049 a| EREEa| NEHH;

050 00 a| QA564b| .S294 2010;

082 00 a| 516.3/522| 22;

100 1 a| Schertz, Reinhard,d| 1943-?| UNAUTHORIZED;

245 10 a| Complex multiplicationh| [electronic resource] /c| Reinhard Schertz.;

260 a| Cambridge, UK ;a| New York :b| Cambridge University Press,;

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.;

506 a| Available only to authorized users.;

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.;

538 a| Mode of access: World Wide Web;

650 0 a| Multiplication, Complex.=| ^A46572;

655 0 a| Electronic books.=| ^A491897;

830 0 a| New mathematical monographs ;v| 15.=| ^A704413;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=542892;

947 a| (OCoLC)ocn449827362;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

949 a| CLICK ON WEB ADDRESSw| ASISh| JMUSIC60;

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998 a| 4023034;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 4023034-1001l| JNETm| JOYNERr| Ys| Yt| JNESSBKu| 1/1/2016x| EBOOKz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 4023034-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 1/1/2016x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 4023034-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/1/2016x| EBOOKz| JERESOURCE;

Complex multiplication / Reinhard Schertz.

Author/creator	Schertz, Reinhard, 1943-
Format	Electronic
Publication Info	Cambridge, UK ; New York : Cambridge University Press,
Description	xiii, 361 p. : ill. ; 24 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Multiplication, Complex.

Series	New mathematical monographs ; 15 New mathematical monographs ; 15. ^A704413
Contents	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.
Abstract	"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.
Bibliography note	Includes bibliographical references (p. 351-355) and indexes.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2009051874
ISBN	9780521766685 (hardback)

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