The Method of Trigonometrical Sums in the Theory of NumbersCourier Corporation, 30 oct. 2013 - 192 pages 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. |
Autres éditions - Tout afficher
The Method of Trigonometrical Sums in the Theory of Numbers Ivan Matveevich Vinogradov Affichage d'extraits - 1954 |
The Method of Trigonometrical Sums in the Theory of Numbers Ivan Matveevich Vinogradov Affichage d'extraits - 1954 |
The Method of Trigonometrical Sums in the Theory of Numbers Ivan Matveevich Vinogradov Aucun aperçu disponible - 2004 |
Expressions et termes fréquents
15 of Chapter 2b k+h 3n² log a₁ absolute convergence apply Lemma asymptotic formula b₁ basic intervals box of type c₁ Cauchy's inequality corresponding defined denote the number diagonal box equation exponential sums Fourier series function g₁ Goldbach's Problem Hardy and Littlewood Hence Hölder's inequality hypotheses interval of length Lemma 16 Lemma 8a log 12n log q M₁ Math method mod q N₁ notation NOTES ON CHAPTER number g number of points number of possible number of representations number of sets number of solutions number of values obtain p₁ polynomial prime factors prove real number runs S₁ S₂ sequence set of residues soluble sufficiently large summation supplementary intervals Suppose T₁ Theorem 2a theory of numbers U₁ v₁ variables Vinogradov Vorlesungen über Zahlentheorie Waring's Problem Weyl sums x₁ y₁ þ₁ Σ Σ Σ φτ