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Éléments de théorie des nombres. (Elements of number theory). (French) Zbl 0584.10001

Mathématiques. Paris: Presses Universitaires de France. 279 p. FF 180.00 (1986).
This book is an introduction to the main domains in Number Theory: Diophantine approximations in \({\mathbb{R}}\) and in \({\mathbb{R}}^ n\), absolute values and p-adic numbers, quadratic forms in \({\mathbb{Q}}\) and \({\mathbb{Q}}_ p\), number fields (integers, units, factorization in the rings of integers, discriminant and ramification), distribution of prime numbers.
Each of the eight chapters is followed by a lot of exercises. In each domain, all the definitions and basic results are given so that every Mathematician can read the book easily. It may be particularly helpful for students interested in research around Number Theory (and also students preparing the French Agregation).
Reviewer: A.Escassut

MSC:

11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
12-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory