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: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
©2010.
|
| Schriftenreihe: | New mathematical monographs ;
15. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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: | 1 online resource (xiii, 361 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 351-355) and indexes. |
| ISBN: | 9780511776199 0511776195 9780511773617 0511773617 9780511776892 0511776896 9781107471771 110747177X 1107208912 9781107208919 1139636669 9781139636667 1282651862 9781282651869 9786612651861 6612651865 0511775431 9780511775437 0511772548 9780511772542 0511774672 9780511774676 |
Internformat
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| 245 | 1 | 0 | |a Complex multiplication / |c Reinhard Schertz. |
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| 490 | 1 | |a New mathematical monographs ; |v 15 | |
| 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 | ||
| 504 | |a Includes bibliographical references (pages 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. | |
| 588 | 0 | |a Print version record. | |
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| author | Schertz, Reinhard, 1943- |
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| 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. |
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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</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 351-355) and indexes.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="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. 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| genre | Electronic book. Electronic books. |
| genre_facet | Electronic book. Electronic books. |
| id | ZDB-4-EBA-ocn649480138 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:22Z |
| institution | BVB |
| isbn | 9780511776199 0511776195 9780511773617 0511773617 9780511776892 0511776896 9781107471771 110747177X 1107208912 9781107208919 1139636669 9781139636667 1282651862 9781282651869 9786612651861 6612651865 0511775431 9780511775437 0511772548 9780511772542 0511774672 9780511774676 |
| language | English |
| oclc_num | 649480138 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 361 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | New mathematical monographs ; |
| series2 | New mathematical monographs ; |
| spelling | Schertz, Reinhard, 1943- https://id.oclc.org/worldcat/entity/E39PBJpPy3FqfpY7B3ykcxf8YP http://id.loc.gov/authorities/names/n2009079062 Complex multiplication / Reinhard Schertz. Cambridge ; New York : Cambridge University Press, ©2010. 1 online resource (xiii, 361 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda New mathematical monographs ; 15 "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 Includes bibliographical references (pages 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. Print version record. English. Multiplication, Complex. http://id.loc.gov/authorities/subjects/sh85088383 Multiplication complexe. MATHEMATICS Geometry Algebraic. bisacsh Multiplication, Complex fast Komplexe Multiplikation gnd http://d-nb.info/gnd/4164903-5 Elliptische Funktion gnd Modulfunktion gnd http://d-nb.info/gnd/4039855-9 Electronic book. Electronic books. Print version: Schertz, Reinhard, 1943- Complex multiplication. Cambridge, UK ; New York : Cambridge University Press, 2010 9780521766685 (DLC) 2009051874 (OCoLC)449827362 New mathematical monographs ; 15. http://id.loc.gov/authorities/names/n2003010567 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=323987 Volltext |
| spellingShingle | Schertz, Reinhard, 1943- Complex multiplication / New mathematical monographs ; 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. Multiplication, Complex. http://id.loc.gov/authorities/subjects/sh85088383 Multiplication complexe. MATHEMATICS Geometry Algebraic. bisacsh Multiplication, Complex fast Komplexe Multiplikation gnd http://d-nb.info/gnd/4164903-5 Elliptische Funktion gnd Modulfunktion gnd http://d-nb.info/gnd/4039855-9 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85088383 http://d-nb.info/gnd/4164903-5 http://d-nb.info/gnd/4039855-9 |
| 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. http://id.loc.gov/authorities/subjects/sh85088383 Multiplication complexe. MATHEMATICS Geometry Algebraic. bisacsh Multiplication, Complex fast Komplexe Multiplikation gnd http://d-nb.info/gnd/4164903-5 Elliptische Funktion gnd Modulfunktion gnd http://d-nb.info/gnd/4039855-9 |
| topic_facet | Multiplication, Complex. Multiplication complexe. MATHEMATICS Geometry Algebraic. Multiplication, Complex Komplexe Multiplikation Elliptische Funktion Modulfunktion Electronic book. Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=323987 |
| work_keys_str_mv | AT schertzreinhard complexmultiplication |