On sums of five almost equal prime squares
On sums of four cubes of polynomials
On sums of powers and a related problem
On sums of primes from Beatty sequences.
On sums of sequences of integers, I
On sums of seven cubes of almost primes
On Sums of Squares in etc
On Sums of Two Coprime k-th Powers.
On sums of two cubes: an Ω₊-estimate for the error term
The arithmetic function counts the number of ways to write a natural number n as a sum of two kth powers (k ≥ 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of leads in a natural way to a certain error term which is known to be in mean-square. In this article it is proved that as t → ∞. Furthermore, it is shown that a similar result would be true for every fixed k > 3 provided that a certain set of algebraic numbers contains a sufficiently...
On sums of two kth powers: a mean-square asymptotics over short intervals
On sums of two kth powers: an asymptotic formula for the mean square of the error term
On the additive complements of the primes and sets of similar growth
On the additive completion of primes
On the almost Goldbach problem of Linnik
Under the Generalized Riemann Hypothesis, it is proved that for any there is depending on only such that every even integer is a sum of two odd primes and powers of .
On the asymmetric divisor problem with congruence conditions
A certain generalized divisor function is studied which counts the number of factorizations of a natural number into integer powers with prescribed exponents under certain congruence restrictions. An -estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.
On the asymptotics of the number of p̅-core partitions of integers
On the average order of the lattice rest of a convex body
On the Bombieri-Korobov estimate for Weyl sums
On the circle problem with general weight
On the circle problem with polynomial weight