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