Ternary additive problems of Waring's type.
Sums of Four Cubes.
A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem
On Waring's problem for two cubes and two small cubes
A sieve approach to the Waring-Goldbach problem. I. Sums of four cubes
Sums of Squares Coprime in Pairs
Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.
Lagrange's Four Squares Theorem with almost prime variables.
The localisation of primes in arithmetic progressions of irrational modulus
A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
Goldbach numbers in sparse sequences
We show that for almost all , the inequality has solutions with odd prime numbers and , provided . Moreover, we give a rather sharp bound for the exceptional set. This result provides almost-all results for Goldbach numbers in sequences rather thinner than the values taken by any polynomial.
Exponential sums and additive problems involving square-free numbers
Cubic moments of Fourier coefficients and pairs of diagonal quartic forms
We establish the non-singular Hasse principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensional 21st moment of quartic smooth Weyl sums via a novel cubic moment of Fourier coefficients.
Additive representation in thin sequences, I : Waring's problem for cubes
Piatetski-Shapiro sequences
Sums of three cubes in three linked three-progressions.
Page 1