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.
On the number of representations of integers by quadratic forms in twelve variables.
On the number of representations of integers by some quadratic forms in ten variables.
On the number of representations of positive integers by a direct sum of binary quadratic forms with discriminant .
On the number of representations of positive integers by the quadratic form .
On the product of three homogeneous linear forms
On the representation of numbers by the direct sums of some quaternary quadratic forms.
On the two-dimensional theta functions of the Borweins
On universal binary Hermitian forms.