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 Pythagoras number of a real irreducible algebroid curve.
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 ≢...
On the representation of numbers by positive diagonal quadratic forms with five variables of level 16.
On the representation of numbers by the direct sums of some binary quadratic forms.
On the representation of numbers by the direct sums of some quaternary quadratic forms.
On the sum of two integral squares in quadratic fields ℚ(√±p)
On the theory of cubic residues and nonresidues
On the two-dimensional theta functions of the Borweins