The Method of Trigonometrical Sums in the Theory of Numbers

Nonfiction, Science & Nature, Mathematics, Trigonometry
Cover of the book The Method of Trigonometrical Sums in the Theory of Numbers by I. M. Vinogradov, Dover Publications
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Author: I. M. Vinogradov ISBN: 9780486154527
Publisher: Dover Publications Publication: October 30, 2013
Imprint: Dover Publications Language: English
Author: I. M. Vinogradov
ISBN: 9780486154527
Publisher: Dover Publications
Publication: October 30, 2013
Imprint: Dover Publications
Language: English
Since the 1930s, the analytic theory of numbers has been transformed by the influence of I. M. Vinogradov, and this text for upper-level undergraduates and graduate students testifies to its author's ingenuity and to the effectiveness of his methods. Starting with a discussion of general lemmas, it advances to an investigation of Waring's problem, including explorations of singular series, the contribution of the basic intervals, and an estimate for G(n). Further topics include approximation by the fractional parts of the values of a polynomial, estimates for Weyl sums, the asymptotic formula in Waring's problem, the distribution of the fractional parts of the values of a polynomial, estimates for the simplest trigonometrical sums with primes, and Goldbach's problem. 1954 edition.
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Since the 1930s, the analytic theory of numbers has been transformed by the influence of I. M. Vinogradov, and this text for upper-level undergraduates and graduate students testifies to its author's ingenuity and to the effectiveness of his methods. Starting with a discussion of general lemmas, it advances to an investigation of Waring's problem, including explorations of singular series, the contribution of the basic intervals, and an estimate for G(n). Further topics include approximation by the fractional parts of the values of a polynomial, estimates for Weyl sums, the asymptotic formula in Waring's problem, the distribution of the fractional parts of the values of a polynomial, estimates for the simplest trigonometrical sums with primes, and Goldbach's problem. 1954 edition.

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