The Hardy-Littlewood MethodCambridge University Press |
Table des matières
Introduction and historical background | 1 |
The simplest upper bound for Gk | 8 |
Goldbachs problems | 27 |
The major arcs in Warings problem | 38 |
5 Vinogradovs methods | 57 |
6 Davenports methods | 94 |
7 Vinogradovs upper bound for Gk | 111 |
8 A ternary additive problem | 127 |
9 Homogeneous equations and Birchs theorem | 147 |
10 A theorem of Roth | 155 |
11 Diophantine inequalities | 167 |
12 Wooleys upper bound for Gk | 175 |
Bibliography | 195 |
| 229 | |
Expressions et termes fréquents
a₁ a₂ Acta Arith Acta Math Akad algebraic number fields an)da argument Arhipov arithmetic progressions asymptotic formula B₁ Brüdern C₁ Cauchy's inequality Chowla Chubarikov congruence cubes Davenport denote the number Diophantine equations Diophantine inequalities Estermann estimate follows function gives Goldbach's h₁ h₂ Hardy Hardy-Littlewood method Hence Hölder's inequality Hua's lemma induction integers k₁ kth power residues Lemma Littlewood Lond m₁ major arcs Mathematika mean value theorem minor arcs modulo Moreover natural numbers Nauk SSSR non-trivial number of choices number of solutions Parseval's identity Philos polynomial positive number Proc proof of Theorem q₁ real number reine angew representation of integers residue classes satisfies Show summation Suppose Theorem 6.2 trivial U₁ V₁ variables Vaughan Waring's problem Weyl's inequality Wooley x₁ y₁ Z₁