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Viser: Number Theory - Analytic and Modern Tools
Number Theory
Analytic and Modern Tools
Henri Cohen
(2007)
Sprog: Engelsk
Springer New York
571,00 kr.
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Detaljer om varen
- 1. Udgave
- Hardback: 596 sider
- Udgiver: Springer New York (Maj 2007)
- ISBN: 9780387498935
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 local aspect, global aspect, and 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.
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.
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