Quadratic forms and biquadratic reciprocity.
Quadratic forms and four partition functions modulo 3.
Quadratic forms between Euclidean Spheres.
Quadratsummen in totalreellen algebraischen Zahlkörpern.
Ramanujan identities and Euler products for a type of Dirichlet series
Recursive determination of the enumerator for sums of three squares.
Remarque au sujet de la fonction qui exprime la somme des diviseurs de .
Remarques sur la théorie des nombres et sur les fractions continues.
Representation by quadratic forms in valuation rings
Representation numbers of five sextenary quadratic forms
For nonnegative integers a, b, c and positive integer n, let N(a,b,c;n) denote the number of representations of n by the form . Explicit formulas for N(a,b,c;n) for some small values were determined by Alaca, Alaca and Williams, by Chan and Cooper, by Köklüce, and by Lomadze. We establish formulas for N(2,1,0;n), N(2,0,1;n), N(1,2,0;n), N(1,0,2;n) and N(1,1,1;n) by employing the (p, k)-parametrization of three 2-dimensional theta functions due to Alaca, Alaca and Williams.
Representation of integers by Hermitian forms.
Representation of prime powers in arithmetical progressions by binary quadratic forms
Let be a set of binary quadratic forms of the same discriminant, a set of arithmetical progressions and a positive integer. We investigate the representability of prime powers lying in some progression from by some form from .
Representations by quaternary quadratic forms whose coefficients are 1, 3 and 9
Representations by sextenary quadratic forms whose coefficients are 1, 2 and 4
Representations of non-negative polynomials via KKT ideals
This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush-Kuhn-Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K.
Representations of squares by certain quinary quadratic forms
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