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The prime numbers. (Les nombres premiers.) (French) Zbl 0867.11002
Que sais-je? Paris: Presses Universitaires de France. 127 p. (1997).
In the same collection “Que sais-je?” was published in 1953 a small monograph about primes by E. Borel [see Zbl 0053.36001]. A new edition by J. Itard, focusing on the algebraic methods, was published in 1969 [see Zbl 0197.32303]. The present edition, with the same title, is, however, completely different. It intends to present analytical number theory. The following is a short table of contents: Notations and conventions; Chapter I. Genesis: From Euclid to Tchebychev (Chebyshev); Chapter II. The Riemann zeta function; Chapter III. Stochastic distribution of primes; Chapter IV. An elementary proof of the prime number theorem and Chapter V. The great conjectures.
Although the collection is intended to publish books on vulgarisation, this one, as the authors say in their preface, is certainly not. However, it can be read in “diagonal” by omitting the proofs when they seem difficult. The reviewer recommends it to all interested readers.

MSC:
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11A41 Primes
11N05 Distribution of primes
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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