Integral Solution of Hilbert's Seeventeenth Problem.
Kaplansky's ternary quadratic form.
Linear relations among theta series of genera of ternary forms
Minimal -universality criteria may vary in size
In this note, we give simple examples of sets of quadratic forms that have minimal -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.
Modular properties of theta-functions and representation of numbers by positive quadratic forms.
Nineteen quaternary quadratic forms
Note zu der Abhandlung über ternäre Formen im 98. Bande dieses Journals.
Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs.
Nouvelles applications des paramètres continus à théorie des formes quadratiques. Deuxième Mémoire. Recherches sur les paralléloèdres primitifs.
O minimu forem kvadratických
On a class of positive semidefinite biquadratic forms. (Sur une classe de formes biquadratiques semi-définies positives.)
On a theorem of Waldspurger and on Eisenstein series of Klingen type.
On certain problems in the analytical arithmetic of quadratic forms arising from the theory of curves of genus 2 with elliptic differentials.
On entire modular forms of half-integral weight on the congruence subgroup .
On representing the multiple of a number by a quadratic form
On some universal sums of generalized polygonal numbers
For m = 3,4,... those pₘ(x) = (m-2)x(x-1)/2 + x with x ∈ ℤ are called generalized m-gonal numbers. Sun (2015) studied for what values of positive integers a,b,c the sum ap₅ + bp₅ + cp₅ is universal over ℤ (i.e., any n ∈ ℕ = 0,1,2,... has the form ap₅(x) + bp₅(y) + cp₅(z) with x,y,z ∈ ℤ). We prove that p₅ + bp₅ + 3p₅ (b = 1,2,3,4,9) and p₅ + 2p₅ + 6p₅ are universal over ℤ, as conjectured by Sun. Sun also conjectured that any n ∈ ℕ can be written as and 3p₃(x) + p₅(y) + p₇(z) with x,y,z ∈ ℕ; in...
On the computation of quadratic -class groups
We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer mod and the factorization of , computes the structure of the -Sylow subgroup of the class group of the quadratic order of discriminant in random polynomial time in .
On the dimension of some spaces of generalized ternary theta-series.
On the imbeddings of imaginary quadratic orders in definite quaternion orders.
On the number of representations of a positive integer by certain quadratic forms
For natural numbers a,b and positive integer n, let R(a,b;n) denote the number of representations of n in the form . Lomadze discovered a formula for R(6,0;n). Explicit formulas for R(1,5;n), R(2,4;n), R(3,3;n), R(4,2;n) and R(5,1;n) are determined in this paper by using the (p;k)-parametrization of theta functions due to Alaca, Alaca and Williams.