Introduction to analytic and probabilistic number theory. 2ème éd. (Introduction à la théorie analytique et probabiliste des nombres.) (French) Zbl 0880.11001

This second French edition of G. Tenenbaum’s most welcome monograph on elementary analytic and probabilistic number theory, which corresponds to the English edition [Cambridge Univ. Press (1995; Zbl 0831.11001)], is a revised version of the first edition (see Zbl 0788.11001).
The book contains an enormous wealth of results, ideas and methods from number theory, many difficult exercises and informative notes.
More detailed information about the book may be found in Zbl 0788.11001 and Zbl 0831.11001. The first-mentioned review ends with “This is altogether a worthy and useful addition to the collection of books on analytic number theory,” and the reviewer would like to add: It is a must for mathematicians interested in [analytic] number theory.
Reviewer’s remark: In the meantime, solutions to the exercises of the book may be found in “Exercises corrigés de théorie analytique et probabiliste des nombres” by the author, in collaboration with Jie Wu [Soc. Math. Fr. (1996; Zbl 0873.11002)].


11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11N37 Asymptotic results on arithmetic functions
11K65 Arithmetic functions in probabilistic number theory
11N05 Distribution of primes
11N13 Primes in congruence classes
40E05 Tauberian theorems
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11N35 Sieves
11L07 Estimates on exponential sums