The tensor product of exceptional representations on the general linear group
The terms in Lucas sequences: an algorithm and applications to diophantine equations
The terms in Lucas sequences divisible by their indices.
The terms of the form 7kx² in the generalized Lucas sequence with parameters P and Q
Let Vₙ(P,Q) denote the generalized Lucas sequence with parameters P and Q. For all odd relatively prime values of P and Q such that P² + 4Q > 0, we determine all indices n such that Vₙ(P,Q) = 7kx² when k|P. As an application, we determine all indices n such that the equation Vₙ = 21x² has solutions.
The ternary Goldbach problem.
The object of this paper is to present new proofs of the classical ternary theorems of additive prime number theory. Of these the best known is Vinogradov's result on the representation of odd numbers as the sums of three primes; other results will be discussed later. Earlier treatments of these problems used the Hardy-Littlewood circle method, and are highly analytical. In contrast, the method we use here is a (technically) elementary deduction from the Siegel-Walfisz Prime Number Theory. It uses...
The ternary Goldbach problem in arithmetic progressions
For a large odd integer N and a positive integer r, define b = (b₁,b₂,b₃) and It is known that . Let ε > 0 be arbitrary and . We prove that for all positive integers r ≤ R, with at most exceptions, the Diophantine equation ⎧N = p₁+p₂+p₃, ⎨ j = 1,2,3,⎩ with prime variables is solvable whenever b ∈ (N,r), where A > 0 is arbitrary.
The theory of asymptotic distribution modulo one
The Theta Correspondence and Harmonic Forms. I.
The Theta Correspondence and Harmonic Forms. II.
The three-dimensional Gauss algorithm is strongly convergent almost everywhere.
The topological structure of the set of subsums of an infinite series
The topology of rational points.
The torsion elements in K₂ of some local fields
The torsion subgroup of a family of elliptic curves over the maximal abelian extension of
We determine explicitly the structure of the torsion group over the maximal abelian extension of and over the maximal -cyclotomic extensions of for the family of rational elliptic curves given by , where is an integer.
The totally real extension of degree 6 with minimum discriminant.
The totally real extension of degree 6 with minimum discriminant.
The Trace of Hecke Operators.
The transcendence of certain quasi-periods associated with abelian functions in two variables
The Tribonacci substitution.
The triple, quintuple and setuple product identities revisited.