On the number of representations of a positive integer by a binary quadratic form
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 n by ax² + bxy + cy²
On the number of representations of n by ax²+by(y-1)/2, ax²+by(3y-1)/2 and ax(x-1)/2+by(3y-1)/2
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 quadratic forms as the basis of the space .
On the number of representations of positive integers by the quadratic form .
On the number of square classes of a field of finite level.
On the orthogonal groups of unimodular quadratic forms. II.
On the Pellian equation and the class number of indefinite binary quadratic forms.
On the Poincaré series for diagonal forms over algebraic number fields
On the Poles of Andranov L-Functions.
On the Prime Ideal of an Ordering of Higher Level.
On the product of three homogeneous linear forms
On the properties of invariants of forms.
On the Pythagoras number of a real irreducible algebroid curve.
On the quartic character of quadratic units.
On the quartic character of quadratic units
Let ℤ be the set of integers, and let (m,n) be the greatest common divisor of integers m and n. Let p be a prime of the form 4k+1 and p = c²+d² with c,d ∈ ℤ, and c ≡ d₀ ≡ 1 (mod 4). In the paper we determine for p = x²+(b²+4α)y² (b,x,y ∈ ℤ, 2∤b), and for p = x²+(4a²+1)y² (a,x,y∈ℤ) on the condition that (c,x+d) = 1 or (d₀,x+c) = 1. As applications we obtain the congruence for and the criterion for (if p ≡ 1 (mod 8)), where Uₙ is the Lucas sequence given by U₀ = 0, U₁ = 1 and , and b ≢...