On pairs of additive cubic equations.
On representations of numbers by sums of squares and quadratic fields
On some topics connected with Waring's problem.
On sums of four cubes of polynomials
On sums of seven cubes of almost primes
On Sums of Squares in etc
On the Bombieri-Korobov estimate for Weyl sums
On the counting function for sums of two squares
On the Fourier coefficients of small positive powers of 0 ... .
On the intervals between numbers that are sums of two squares. III.
On the number of integers which are sums of two squares
On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression
We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer in the form with prime numbers such that , under suitable hypothesis on for every integer .
On the numbers that are representable as the sum of two cubes.
On the p-adic Waring's problem
On the representation of cyclotomic polynomials as sums of squares
On the representations of a number as a sum of squares
On the restricted Waring problem over
1. Introduction. The Waring problem for polynomial cubes over a finite field F of characteristic 2 consists in finding the minimal integer m ≥ 0 such that every sum of cubes in F[t] is a sum of m cubes. It is known that for F distinct from ₂, ₄, , each polynomial in F[t] is a sum of three cubes of polynomials (see [3]). If a polynomial P ∈ F[t] is a sum of n cubes of polynomials in F[t] such that each cube A³ appearing in the decomposition has degree < deg(P)+3, we say that P is a restricted...
On the sum of two squares and two powers of k
It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2.
On the Waring-Goldbach problem for one square and five cubes in short intervals
Let be a sufficiently large integer. We prove that almost all sufficiently large even integers can be represented as where with .
On the Waring-Goldbach problem with small non-integer exponent