Ternary additive problems of Waring's type.
The application of a new mean value theorem to the fractional parts of polynomials
The average order of two arithmetical functions
The fifth taxicab number is 48988659276962496.
The Galois Cohomology of Pythagorean Fields.
The number of powers of 2 in a representation of large odd integers
The number Γ(k) in Waring's problem
The representation of almost all numbers as sums of unlike powers
We prove in this article that almost all large integers have a representation as the sum of a cube, a biquadrate, ..., and a tenth power.
The sum of divisors of a quadratic form
We study the sum τ of divisors of the quadratic form m₁² + m₂² + m₃². Let . We obtain the asymptotic formula S₃(X) = C₁X³logX + C₂X³ + O(X²log⁷X), where C₁,C₂ are two constants. This improves upon the error term obtained by Guo and Zhai (2012).
The Tarry-Escott and the "easier" Waring problems.
The Waring-Goldbach problem for cubes
Theoreme de Pfister pour les varietes et anneaux de Witt reduits.
Théorèmes généraux sur l'impossibilité des équations cubiques indéterminées