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81. Number Theory: Volume II: Analytic andModern Tools (Graduate Texts in Mathematics) by Henri Cohen | |
Hardcover: 596
Pages
(2007-05-23)
list price: US$64.95 -- used & new: US$45.20 (price subject to change: see help) Asin: 0387498931 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book deals with several aspects of what is now called "explicit number theory." The central theme 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 of its most basic 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 aspect is the global aspect: the use of number fields, and in particular of class groups and unit groups. The third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject, and embodies in a beautiful way the local and global aspects of Diophantine problems. In fact, these functions are defined through the local aspects of the problems, but their analytic behavior is intimately linked to the global aspects. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included 5 appendices on these techniques. These appendices were written by Henri Cohen, Yann Bugeaud, Maurice Mignotte, Sylvain Duquesne, and Samir Siksek, and contain material on the use of Galois representations, the superfermat equation, Mihailescu’s proof of Catalan’s Conjecture, and applications of linear forms in logarithms. |
82. One equation to rule them all (Rand Corporation. Research memorandum) by Martin Davis | |
Unknown Binding: 12
Pages
(1968)
Asin: B0007FTZO0 Canada | United Kingdom | Germany | France | Japan | |
83. Prime solutions of indeterminate equation w²=x²+y²+z² for all values of w=1 to 100 by Solomon Achillovich Joffe | |
Unknown Binding:
Pages
(1914)
Asin: B000890GNY Canada | United Kingdom | Germany | France | Japan | |
84. The Pell equation by Edward Everett Whitford | |
Unknown Binding: 193
Pages
(1912)
Asin: B000865I9O Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
85. Applications of PadeÌ approximations to diophantine inequalities in values of G-function (Research report RC. International Business Machines Corporation. Research Division) by D Chudnovsky | |
Unknown Binding: 43
Pages
(1985)
Asin: B000718V0I Canada | United Kingdom | Germany | France | Japan | |
86. On the problem 5/n = 1/x + 1/y + 1/z by C. B Glavas | |
Unknown Binding: 39
Pages
(1987)
Asin: B0007CC8VU Canada | United Kingdom | Germany | France | Japan | |
87. Measure Theoretic Laws for Lim Sup Sets (Memoirs of the American Mathematical Society) by Detta Dickinson, and Sanju Velani Victor Beresnevich | |
Paperback: 91
Pages
(2005-12-01)
list price: US$61.00 -- used & new: US$43.15 (price subject to change: see help) Asin: 082183827X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
88. Geodesic and Horocyclic Trajectories (Universitext) by Françoise DalBo | |
Paperback: 157
Pages
(2010-12-03)
list price: US$59.95 -- used & new: US$53.11 (price subject to change: see help) Asin: 085729072X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
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