The Resource Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)

Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)

Label
Number Theory : Volume II: Analytic and Modern Tools
Title
Number Theory
Title remainder
Volume II: Analytic and Modern Tools
Statement of responsibility
by Henri Cohen
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
Member of
Is Subseries of
http://library.link/vocab/creatorName
Cohen, Henri
Dewey number
512.7
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
olgSLKPjyGo
Image bit depth
0
Language note
English
LC call number
QA241-247.5
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Graduate Texts in Mathematics,
Series volume
240
http://library.link/vocab/subjectName
  • Number theory
  • Algorithms
  • Field theory (Physics)
  • Computer science
  • Algebra
  • Number Theory
  • Algorithms
  • Field Theory and Polynomials
  • Computational Mathematics and Numerical Analysis
  • Order, Lattices, Ordered Algebraic Structures
Label
Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
Analytic Tools -- Bernoulli Polynomials and the Gamma Function -- Dirichlet Series and L-Functions -- p-adic Gamma and L-Functions -- Modern Tools -- Applications of Linear Forms in Logarithms -- Rational Points on Higher-Genus Curves -- The Super-Fermat Equation -- The Modular Approach to Diophantine Equations -- Catalan’s Equation
Dimensions
unknown
Edition
1st ed. 2007.
Extent
1 online resource (XXIII, 596 p.)
File format
multiple file formats
Form of item
online
Isbn
9780387498942
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-49894-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000546310
  • (SSID)ssj0000319229
  • (PQKBManifestationID)11937712
  • (PQKBTitleCode)TC0000319229
  • (PQKBWorkID)10337371
  • (PQKB)10996842
  • (DE-He213)978-0-387-49894-2
  • (MiAaPQ)EBC3063895
  • (EXLCZ)991000000000546310
Label
Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
Analytic Tools -- Bernoulli Polynomials and the Gamma Function -- Dirichlet Series and L-Functions -- p-adic Gamma and L-Functions -- Modern Tools -- Applications of Linear Forms in Logarithms -- Rational Points on Higher-Genus Curves -- The Super-Fermat Equation -- The Modular Approach to Diophantine Equations -- Catalan’s Equation
Dimensions
unknown
Edition
1st ed. 2007.
Extent
1 online resource (XXIII, 596 p.)
File format
multiple file formats
Form of item
online
Isbn
9780387498942
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-49894-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000546310
  • (SSID)ssj0000319229
  • (PQKBManifestationID)11937712
  • (PQKBTitleCode)TC0000319229
  • (PQKBWorkID)10337371
  • (PQKB)10996842
  • (DE-He213)978-0-387-49894-2
  • (MiAaPQ)EBC3063895
  • (EXLCZ)991000000000546310

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