Sums of squares, cubes, and higher powers.
Sums of squares in
Sums of squares in rings of integers with 2 inverted
We prove that in a ring of S-integers containing 1/2, any totally positive element is a sum of five squares. We also exhibit examples of such rings where some totally positive elements cannot be written as the sum of four squares.
Sums of three cubes, II
Estimates are provided for sth moments of cubic smooth Weyl sums, when 4 ≤ s ≤ 8, by enhancing the author's iterative method that delivers estimates beyond classical convexity. As a consequence, an improved lower bound is presented for the number of integers not exceeding X that are represented as the sum of three cubes of natural numbers.
Sums of three cubes in three linked three-progressions.
Sums of three squares in certain Cayley rings
Sums of two k th powers.
Sums of two relatively prime cubes
Sums of values of a rational function
Sumsets avoiding squarefree integers
Sumsets containing long arithmetic progressions and powers of 2
Sumsets of finite Beatty sequences.
Sum-sets of small upper density
Sur certaines hypothèses concernant les nombres premiers
Sur la constante de Šnirel'man
Sur la décomposition d'un entier en une somme de puissances huitièmes d'entiers (Problème de Waring)
Sur la démonstration de l'hypothèse de Goldbach pour les nombres impairs, donnée par M. Vinogradow
Sur la fonction de répartition de certaines fonctions arithmétiques définies sur l'ensemble des nombres premiers moins un
Sur la majoration de sommes de Weyl biquadratiques
Sur la partition des nombres.