Number Theory (Record no. 369545)

000 -LEADER
fixed length control field 04143nam a22005415i 4500
001 - CONTROL NUMBER
control field 978-0-387-49923-9
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20180115171410.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 100301s2007 xxu| s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780387499239
-- 978-0-387-49923-9
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-0-387-49923-9
Source of number or code doi
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA241-247.5
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBH
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT022000
Source bisacsh
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.7
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Cohen, Henri.
Relator term author.
245 10 - TITLE STATEMENT
Title Number Theory
Medium [electronic resource] :
Remainder of title Volume I: Tools and Diophantine Equations /
Statement of responsibility, etc. by Henri Cohen.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture New York, NY :
Name of producer, publisher, distributor, manufacturer Springer New York,
Date of production, publication, distribution, manufacture, or copyright notice 2007.
300 ## - PHYSICAL DESCRIPTION
Extent XXIII, 650 p.
Other physical details online resource.
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
347 ## - DIGITAL FILE CHARACTERISTICS
File type text file
Encoding format PDF
Source rda
490 1# - SERIES STATEMENT
Series statement Graduate Texts in Mathematics,
International Standard Serial Number 0072-5285 ;
Volume/sequential designation 239
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note to Diophantine Equations -- to Diophantine Equations -- Tools -- Abelian Groups, Lattices, and Finite Fields -- Basic Algebraic Number Theory -- p-adic Fields -- Quadratic Forms and Local-Global Principles -- Diophantine Equations -- Some Diophantine Equations -- Elliptic Curves -- Diophantine Aspects of Elliptic Curves.
520 ## - SUMMARY, ETC.
Summary, etc. The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the third part of the book, including many interesting and original applications. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. These chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, Samir Siksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms. The book contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and contain many important additional results.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Algebra.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Field theory (Physics).
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Ordered algebraic structures.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computer mathematics.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Algorithms.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Number theory.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Number Theory.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Algorithms.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Field Theory and Polynomials.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computational Mathematics and Numerical Analysis.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Order, Lattices, Ordered Algebraic Structures.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9780387499222
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Graduate Texts in Mathematics,
International Standard Serial Number 0072-5285 ;
Volume number/sequential designation 239
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="http://dx.doi.org/10.1007/978-0-387-49923-9">http://dx.doi.org/10.1007/978-0-387-49923-9</a>
912 ## -
-- ZDB-2-SMA
Holdings
Withdrawn status Lost status Damaged status Not for loan Collection code Permanent Location Current Location Date acquired Date last seen Price effective from Koha item type
  Not Lost     EBook e-Library e-Library 2018-01-15 2018-01-15 2018-01-15 eBook

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