Some problems about the ternary quadratic form m₁² + m₂² + m₃²
Summation of singular series corresponding to representations of numbers by some quadratic forms in twelve variables.
Summation of singular series corresponding to the representation of integers by some quadratic forms in fourteen variables.
Sums of nine squares
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 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 squares of integral linear forms
Sums of twelve squares
Supplements to the theory of quartic residues
Sur la décomposition d'un nombre en quatre carrés
Sur la décomposition en carrés des nombres premiers de la forme
Sur la forme ternaire .
Sur les formes d’Hermite ternaires dans un corps quadratique imaginaire (champs et )
Sur les nombres de la forme
Sur quelques applications de la théorie des fonctions elliptiques à la théorie des nombres (suite et fin)
Sur quelques applications de la théorie des fonctions elliptiques à la théorie des nombres
Sur quelques formules générales qui se rattachent à certaines formes quadratiques (premier article).
Ternary positive quadratic forms that represent all odd positive integers
Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4
Under the assumption that the ternary form x² + 2y² + 5z² + xz represents all odd positive integers, we prove that a ternary quadratic form ax² + by² + cz² (a,b,c ∈ ℕ) represents all positive integers n ≡ 4(mod 8) if and only if it represents the eight integers 4,12,20,28,52,60,140 and 308.