Additive number theory: the classical bases / Melvyn B. Nathanson

Auteur: Nathanson, Melvyn Bernard (1944-) - AuteurType de document: MonographieCollection: Graduate texts in mathematics ; 164Langue: anglaisPays: Etats UnisÉditeur: New York : Springer-Verlag, 1996Description: 1 vol. (XIV-342 p.) : ill. ; 25 cm ISBN: 9780387946566 ; rel. Note: This book, intended for graduate students, is principally concerned with the problems of Waring and Goldbach. The general theory of additive bases receives virtually no discussion. The topics covered are: sums of polygonal numbers; elementary results on Waring's problem, including Hilbert's work; the Hardy-Littlewood method; estimates for primes; Brun's theorem on twin primes; the Selberg sieve; Shnirelʹman's theorem on the Goldbach problem; Vinogradov's 3 primes theorem; the linear sieve; and Chen's theorem. There is also an appendix on arithmetic functions. Each chapter has notes and exercises, though the latter would have benefitted from some more taxing examples. Occasional results, such as the Bombieri-Vinogradov theorem, are used without proof, but the text is essentially self-contained. (MathSciNet)Bibliographie: Bibliogr. p. [331]-339. Index. Sujets MSC: 11P05 Number theory -- Additive number theory; partitions -- Waring's problem and variants
11P32 Number theory -- Additive number theory; partitions -- Goldbach-type theorems; other additive questions involving primes
11P55 Number theory -- Additive number theory; partitions -- Applications of the Hardy-Littlewood method
11Pxx Number theory -- Additive number theory; partitions
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This book, intended for graduate students, is principally concerned with the problems of Waring and Goldbach. The general theory of additive bases receives virtually no discussion.
The topics covered are: sums of polygonal numbers; elementary results on Waring's problem, including Hilbert's work; the Hardy-Littlewood method; estimates for primes; Brun's theorem on twin primes; the Selberg sieve; Shnirelʹman's theorem on the Goldbach problem; Vinogradov's 3 primes theorem; the linear sieve; and Chen's theorem. There is also an appendix on arithmetic functions. Each chapter has notes and exercises, though the latter would have benefitted from some more taxing examples. Occasional results, such as the Bombieri-Vinogradov theorem, are used without proof, but the text is essentially self-contained. (MathSciNet)

Bibliogr. p. [331]-339. Index

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