Primes of the Form X2+ny2 : (Record no. 39684)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05302nam a22004573i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC1771572 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729123007.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2013 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781118400753 |
| Qualifying information | (electronic bk.) |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC1771572 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL1771572 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr10915810 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)889675019 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA246 -- .C69 2013eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.723 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Cox, David A. |
| 245 10 - TITLE STATEMENT | |
| Title | Primes of the Form X2+ny2 : |
| Remainder of title | Fermat, Class Field Theory, and Complex Multiplication. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2nd ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Newark : |
| Name of producer, publisher, distributor, manufacturer | John Wiley & Sons, Incorporated, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2013. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2013. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (378 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Series ; |
| Volume/sequential designation | v.119 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title Page -- Copyright -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Notation -- Introduction -- Chapter One: From Fermat to Gauss -- 1. Fermat, Euler and Quadratic Reciprocity -- A. Fermat -- B. Euler -- C. P = x2 + ny2 and Quadratic Reciprocity -- D. Beyond Quadratic Reciprocity -- E. Exercises -- 2. Lagrange, Legendre and Quadratic Forms -- A. Quadratic Forms -- B. P = x2 + ny2 and Quadratic Forms -- C. Elementary Genus Theory -- D. Lagrange and Legendre -- E. Exercises -- 3. Gauss, Composition and Genera -- A. Composition and the Class Group -- B. Genus Theory -- C. P = x2 + ny2 and Euler's Convenient Numbers -- D. Disquisitiones Arithmeticae -- E. Exercises -- 4. Cubic and Biquadratic Reciprocity -- A. Z[w] and Cubic Reciprocity -- B. Z[i] and Biquadratic Reciprocity -- C. Gauss and Higher Reciprocity -- D. Exercises -- Chapter Two: Class Field Theory -- 5. The Hilbert Class Field and P = x2 + ny2 -- A. Number Fields -- B. Quadratic Fields -- C. The Hilbert Class Field -- D. Solution of P = x2 + ny2 for Infinitely Many n -- E. Exercises -- 6. The Hilbert Class Field and Genus Theory -- A. Genus Theory for Field Discriminants -- B. Applications to the Hilbert Class Field -- 7. Orders in Imaginary Quadratic Fields -- A. Orders in Quadratic Fields -- B. Orders and Quadratic Forms -- C. Ideals Prime to the Conductor -- D. The Class Number -- E. Exercises -- 8. Class Field Theory and the Cebotarev Density Theorem -- A. The Theorems of Class Field Theory -- B. The Čebotarev Density Theorem -- C. Norms and Ideles -- D. Exercises -- 9. Ring Class Fields and p = x2 + ny2 -- A. Solution of p = x2 + ny2 for All n -- B. The Ring Class Fields of Z[√-27] and Z[√-64] -- C. Primes Represented by Positive Definite Quadratic Forms -- D. Ring Class Fields and Generalized Dihedral Extensions -- E. Exercises. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Chapter Three: Complex Multiplication -- 10. Elliptic Functions and Complex Multiplication -- A. Elliptic Functions and the Weierstrass r-function -- B. The J-invariant of a Lattice -- C. Complex Multiplication -- D. Exercises -- 11. Modular Functions and Ring Class Fields -- A. The J-function -- B. Modular Functions for Γo(m) -- C. The Modular Equation Φm(x, y) -- D. Complex Multiplication and Ring Class Fields -- E. Exercises -- 12. Modular Functions and Singular J-invariants -- A. The Cube Root of the J-function -- B. The Weber Functions -- C. J-invariants of Orders of Class Number 1 -- D. Weber's Computation of J (√-14) -- E. Imaginary Quadratic Fields of Class Number 1 -- F. Exercises -- 13. The Class Equation -- A. Computing the Class Equation -- B. Computing the Modular Equation -- C. Theorems of Deuring, Gross and Zagier -- D. Exercises -- Chapter Four: Additional Topics -- 14. Elliptic Curves -- A. Elliptic Curves and Weierstrass Equations -- B. Complex Multiplication and Elliptic Curves -- C. Elliptic Curves over Finite Fields -- D. Elliptic Curve Primality Tests -- E. Exercises -- 15. Shimura Reciprocity -- A. Modular Functions and Shimura Reciprocity -- B. Extended Ring Class Fields -- C. Shimura Reciprocity for Extended Ring Class Fields -- D. Shimura Reciprocity for Ring Class Fields -- E. The Idelic Approach -- F. Exercises -- References -- Additional References -- A. References Added to the Text -- B. Further Reading for Chapter One -- C. Further Reading for Chapter Two -- D. Further Reading for Chapter Three -- E. Further Reading for Chapter Four -- Index. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Numbers, Prime. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Mathematics. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Cox, David A. |
| Title | Primes of the Form X2+ny2 |
| Place, publisher, and date of publication | Newark : John Wiley & Sons, Incorporated,c2013 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=1771572">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=1771572</a> |
| Public note | Click to View |
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