The Method of Trigonometrical Sums in the Theory of Numbers

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 congruence corresponding defined denote the number diagonal box distribution 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 of points number of possible number of representations number of sets number of solutions number of values numbers d obtain P₁ polynomial prime factors prove Pt+1 real number runs S₁ S₂ set of residues sets of values soluble sufficiently large supplementary intervals Suppose T₁ Theorem 2a theory of numbers U₁ v₁ variables Vinogradov Waring's Problem Weyl sums x₁ y₁ Σ Σ φτ