Corrigendum to the paper "Additive problems with prime numbers of special type" (Acta Arith. 96 (2000), 53-88)
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.
Darstellung total positiver ganzer algebraischer Zahlen als Summe N-freier Zahlen
Diagonal cubic equations
Diagonal cubic equations. II
Difference sets and polynomials of prime variables
Difference sets and the primes
Diophantine approximation with primes and powers of two.
Diophantine inequalities for the non-Archimedean line
Distribution of integers that are sums of three squares of primes
Eight cubes of primes and powers of 2
Ein binäres additives Problem.
Equirépartition des solutions du problème de Waring
Évaluation d'une somme arithmétique associée à une forme modulaire non analytique
Exceptional sets in Waring's problem: two squares and s biquadrates
Let denote the number of representations of the positive number n as the sum of two squares and s biquadrates. When or 4, it is established that the anticipated asymptotic formula for holds for all with at most exceptions.
Exponential sums and additive problems involving square-free numbers
Four prime squares and powers of 2
Four squares of primes and 165 powers of 2
Four squares of primes and powers of 2
By developing the method of Wooley on the quadratic Waring-Goldbach problem, we prove that all sufficiently large even integers can be expressed as a sum of four squares of primes and 46 powers of 2.
Further improvements in Waring's problem, IV: Higher powers