Number Theory

• 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.

From the reviews: "Cohen (Universite 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 fur Mathematik, Vol. 157 (2), June, 2009)