Multiplicative number theory / Harold Davenport ; Hugh L. Montgomery, editorType de document : MonographieCollection : Graduate texts in mathematics, 74Langue : anglais.Pays: Etats Unis.Mention d'édition: 2nd editionÉditeur : New York : Springer, 1980Description : 1 vol. (XIII-177 p.) ; 24 cmISBN: 9780387905334.ISSN: 0072-5285.Bibliographie : Bibliogr. p. XI. Index.Sujet MSC : 11Lxx, Number theory - Exponential sums and character sums
11Mxx, Number theory - Zeta and L-functions: analytic theory
11Nxx, Number theory - Multiplicative number theory
11P32, Additive number theory; partitions, Goldbach-type theorems; other additive questions involving primes
11N35, Multiplicative number theory, SievesEn-ligne : Springerlink | Zentralblatt | MathSciNet Item type: Monographie
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This book originated from a lecture series [Multiplicative number theory, Markham, Chicago, Ill., 1967; MR0217022 (36 #117)] of the equally great mathematician and teacher given at the University of Michigan in 1966. Then its main merits were, aiming for the results on the (global) distribution of the primes and the primes in an arithmetic progression (with uniformity with respect to the modulus), to give a straightforward and very clear presentation of the necessary tools and techniques, and making the then most recent form of the large sieve and Bombieri's theorem readily accessible. The subsequent vivid interest in the large sieve and its applications for more than a decade has led to considerable clarification and simplification.
This second edition has been revised with both great expertise and care by Montgomery. According to the preface Sections 23–29 were completely rewritten: now the proof of Bombieri's theorem (Section 28) is based on Vaughan's method (Section 24), a most valuable supplement (also its application to Vinogradov's theorem on sums of three primes is included (Sections 25, 26)). The rest of the book is virtually unchanged but brought up to date: for example, references to more recent work have been added (Sections 3, 9, 14, 18, 21), two refinements due to E. Wirsing (Sections 12, 14) and also a few minor improvements of proofs (Sections 19, 21) included.
Altogether this is an important book which should be a must for anyone who is interested in analytic number theory. (MathSciNet)
Bibliogr. p. XI. Index