Number Theory: Volume II: Analytic and Modern Tools / Edition 1

by Henri Cohen

Overview

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.

Product Details

ISBN-13:	9780387498935
Publisher:	Springer New York
Publication date:	05/28/2007
Series:	Graduate Texts in Mathematics Series , #240
Edition description:	2007
Pages:	596
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

Table of 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.

Editorial Reviews

From the reviews:

"Cohen (Université Bordeaux I, France), an instant classic, uniquely bridges the gap between old-fashioned, naive treatments and the many modern books available that develop the tools just mentioned … . Summing Up: Recommended. … Upper-division undergraduates through faculty." (D. V. Feldman, CHOICE, Vol. 45 (5), January, 2008)

"The book deals with aspects of ‘explicit number theory’. … The central theme … is the solution of Diophantine equations. … It combines an interesting ‘philosophy’ of the subject with an encyclopedic grasp of detail. The extension of the author’s reach via the contributed chapters is a good idea. Perhaps it is the start of a trend, as the subject grows more and more. … It will undoubtedly be mined by instructors for their graduate courses, particularly for the purpose of including some recently-proved content." (R. C. Baker, Mathematical Reviews, Issue 2008 e)

“This is the second volume of a highly impressive two-volume textbook on Diophantine analysis. … readers are presented with an almost overwhelming amount of material. This … text book is bound to become an important reference for students and researchers alike.” (C. Baxa, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)

From the Publisher