Rationals Not Expressible as a Sum of Three Unit Fractions.
Remarks on some new applications of the dispersion method
Representation of a prime as the sum of squares in a tower of fields.
Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids.
Representations of every integer as the difference of nonsquare powerful numbers
Representations of multivariate polynomials by sums of univariate polynomials in linear forms
The paper is concentrated on two issues: presentation of a multivariate polynomial over a field K, not necessarily algebraically closed, as a sum of univariate polynomials in linear forms defined over K, and presentation of a form, in particular a zero form, as the sum of powers of linear forms projectively distinct defined over an algebraically closed field. An upper bound on the number of summands in presentations of all (not only generic) polynomials and forms of a given number of variables and...
Representing integers as linear combinations of S-units
Résolution de l’équation indéterminée en nombres entiers.
Small solutions of quadratic congruences and small fractional parts of quadratic forms
Some Examples of Weber-Hecke Ring Class Field Theory.
Some problems of Waring?s type
Some Recent Developments in three Classical Problems of Number Theory.
Sommes de carrés dans [Book]
Square-free points on ellipsoids
Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
Sums of k-th powers in the ring of polynomials with integer coefficients
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.
Sums of two k th powers.
Sur l'approximation du nombre de solutions de certaines équations diophantiennes
Sur le problème de Waring à exposant réel (résultats de Dress et Polzin)