Number Theory : Volume I: Tools and Diophantine Equations
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The work Number Theory : Volume I: Tools and Diophantine Equations represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Number Theory : Volume I: Tools and Diophantine Equations
Resource Information
The work Number Theory : Volume I: Tools and Diophantine Equations represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Number Theory : Volume I: Tools and Diophantine Equations
 Title remainder
 Volume I: Tools and Diophantine Equations
 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
 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
 239
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