Borrow it
 Architecture Library
 Bizzell Memorial Library
 Boorstin Collection
 Chinese Literature Translation Archive
 Engineering Library
 Fine Arts Library
 Harry W. Bass Business History Collection
 History of Science Collections
 John and Mary Nichols Rare Books and Special Collections
 Library Service Center
 Price College Digital Library
 Western History Collections
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)
Resource Information
The item Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 The central theme of this graduatelevel 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 padic 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 3descent 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 Lfunctions, and of padic 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 highergenus 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
 Language

 eng
 eng
 Edition
 1st ed. 2007.
 Extent
 1 online resource (XXIII, 596 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 Analytic Tools
 Bernoulli Polynomials and the Gamma Function
 Dirichlet Series and LFunctions
 padic Gamma and LFunctions
 Modern Tools
 Applications of Linear Forms in Logarithms
 Rational Points on HigherGenus Curves
 The SuperFermat Equation
 The Modular Approach to Diophantine Equations
 Catalanâ€™s Equation
 Isbn
 9780387498942
 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
 Language

 eng
 eng
 Summary
 The central theme of this graduatelevel 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 padic 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 3descent 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 Lfunctions, and of padic 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 highergenus 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
 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
 QA241247.5
 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)
 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 LFunctions  padic Gamma and LFunctions  Modern Tools  Applications of Linear Forms in Logarithms  Rational Points on HigherGenus Curves  The SuperFermat Equation  The Modular Approach to Diophantine Equations  Catalanâ€™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
 10.1007/9780387498942
 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
 (DEHe213)9780387498942
 (MiAaPQ)EBC3063895
 (EXLCZ)991000000000546310
 Label
 Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)
 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 LFunctions  padic Gamma and LFunctions  Modern Tools  Applications of Linear Forms in Logarithms  Rational Points on HigherGenus Curves  The SuperFermat Equation  The Modular Approach to Diophantine Equations  Catalanâ€™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
 10.1007/9780387498942
 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
 (DEHe213)9780387498942
 (MiAaPQ)EBC3063895
 (EXLCZ)991000000000546310
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
Embed (Experimental)
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/NumberTheoryVolumeIIAnalyticandModern/XFPHveckn0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/NumberTheoryVolumeIIAnalyticandModern/XFPHveckn0/">Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/NumberTheoryVolumeIIAnalyticandModern/XFPHveckn0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/NumberTheoryVolumeIIAnalyticandModern/XFPHveckn0/">Number Theory : Volume II: Analytic and Modern Tools, by Henri Cohen, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>