Seven octonary quadratic forms
Sharp large deviations for gaussian quadratic forms with applications
Sharp large deviations for Gaussian quadratic forms with applications
Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process, and finally of the empirical...
Shifted B-numbers as a set of uniqueness for additive and multiplicative functions
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)