Additive Theory of Prime Numbers |
Contents
Estimates for sums involving the divisor function dn | 11 |
Meanvalue theorems for certain trigonometric sums I | 19 |
Vinogradovs meanvalue theorem and its corollaries | 26 |
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a₁ absolutely convergent accordingly obtain b₁ c₁ C₂ Cauchy's inequality chapter congruence congruent solvability convex function Corollary da₁ denote the number distinct integers equations exponential density Fundamental Lemma Further h₁ Hence we obtain Hölder's inequality I. M. Vinogradov integers satisfying integral-valued polynomial k³ log know by Lemma kth degree least common least common multiple Let f(x log log mod Q N₁ N₂ number of distinct number of sets number of solutions obtain the lemma P₁ positive integer positive number positive solvability prime factors prime numbers proof of Theorem S₁ S₂ set of distinct set of residues sets of integers Suppose t₁ Theorem 11 TRIGONOMETRIC SUMS U(P³ v₁ values Vinogradov x₁ y₁ α₁ Σ Σ ΣΣ ΣΣΣ