On the product of the conjugates outside the unit circle of an algebraic number
On the product of three homogeneous linear forms
On the products of Hecke L-functions of holomorphic cusp forms
On the projective class group of cyclic groups of prime power order.
On the proof of Humbert's volume formula.
On the proof of the prime number theorem
On the properties of invariants of forms.
On the properties of oscillation and almost periodicity of certain convolutions
On the property .
On the pure Jacobi sums
On the Pythagoras number of a real irreducible algebroid curve.
On the Pythagoras number of orders in totally real number fields.
On the -Pell sequences and sums of tails
We examine the -Pell sequences and their applications to weighted partition theorems and values of -functions. We also put them into perspective with sums of tails. It is shown that there is a deeper structure between two-variable generalizations of Rogers-Ramanujan identities and sums of tails, by offering examples of an operator equation considered in a paper published by the present author. The paper starts with the classical example offered by Ramanujan and studied by previous authors noted...
On the q-log-Concavity of Gaussian Binomial Coefficients.
On the quadratic character of some quadratic surds.
On the quadriquadric Curve in connexion with the theory of Elliptic Functions
On the quantitative unit sum number problem-an application of the subspace theorem
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 ≢...
On the quasi-periodic -adic Ruban continued fractions
We study a family of quasi periodic -adic Ruban continued fractions in the -adic field and we give a criterion of a quadratic or transcendental -adic number which based on the -adic version of the subspace theorem due to Schlickewei.