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Le grand crible dans la théorie analytique des nombres. (2e éd. rev. et augmentée). (The large sieve in analytic number theory). (French) Zbl 0618.10042
Astérisque, 18. Publié avec le concours du Centre National de la Recherche Scintifique. Paris: Société Mathématique de France. 103 p.; FF 70.00; $ 11.00 (1987).

[For a review of the first edition (1974) see Zbl 0292.10035.]

In this second edition of the author’s book on the large sieve he added (in English) three sections on some recent developments on the distribution of primes in (large) arithmetic progressions and more general problems, i.e. on general Bombieri-Vinogradov theorems.

The techniques described range from combinatorial identities (Vaughan, Heath-Brown) to use of bilinear forms and Kloosterman sums, and a corresponding list of references has been added.

The short and lucid presentation of this technically involved matter is a valuable extension of the well-known monograph.

Reviewer: H.-E.Richert

MSC:
11N35Sieves
11-02Research monographs (number theory)
11N13Primes in progressions