Quasiconformal analogues of theorems of Koebe and Hardy-Littlewood.

Hardy-Littlewood Theorems for A-Harmonic Tensors

Binary Additive Problems: Theorems of Landau and Hardy-littlewood Type

We prove theorems of Landau and Hardy-Littlewood type for Goldbach, Chen, Lemoime-Levy and other binary partitions of positive integers. We also pose some new conjectures.

On the Hardy - Littlewood majorant

On Permutations of Hardy-littlewood-pólya Sequences

Let H = (q1, . . . , qr) be a finite set of coprime integers and let n1, n2, . . . denote the multiplicative semigroup generated by H and arranged in increasing order. The distribution of such sequences has been studied intensively in number theory, and they have remarkable probabilistic and ergodic properties. In particular, the asymptotic properties of the sequence {nkx} are similar to those ...

Applications of the Hardy - Littlewood Circle Method

1 Waring’s Problem Problem 1. (Waring’s) For every natural number k ≥ 2 there exists a positive integer s such that every natural number is the sum of at most s k powers of natural number (for example, every natural number is the sum of at most 4 squares, or 9 cubes, or 19 fourth powers, etc.). The affirmative answer, known as the Hilbert-Waring theorem, was provided by Hilbert in 1909. Let A =...