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Displaying 941 – 960 of 1341

The Tate pairing for Abelian varieties over finite fields

Peter Bruin (2011)

Journal de Théorie des Nombres de Bordeaux

In this expository note, we describe an arithmetic pairing associated to an isogeny between Abelian varieties over a finite field. We show that it generalises the Frey–Rück pairing, thereby giving a short proof of the perfectness of the latter.

The tensor product of exceptional representations on the general linear group

Anthony C. Kable (2001)

Annales scientifiques de l'École Normale Supérieure

The terms $C x^{h} (h \geq 3)$ in Lucas sequences: an algorithm and applications to diophantine equations

Paulo Ribenboim (2003)

Acta Arithmetica

The terms in Lucas sequences divisible by their indices.

Smyth, Chris (2010)

Journal of Integer Sequences [electronic only]

The terms of the form 7kx² in the generalized Lucas sequence with parameters P and Q

Olcay Karaatlı (2016)

Acta Arithmetica

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.

David Rodney (Roger) Heath-Brown (1985)

Revista Matemática Iberoamericana

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

Jianya Liu, Tao Zhan (1997)

Acta Arithmetica

For a large odd integer N and a positive integer r, define b = (b₁,b₂,b₃) and $(N, r) = b \in ℕ ³ : 1 \leq b_{j} \leq r, (b_{j}, r) = 1 a n d b ₁ + b ₂ + b ₃ \equiv N (m o d r) .$ It is known that $(N, r) = r ² \prod_{p | r} p | N ((p - 1) (p - 2) / p ²) \prod_{p | r} p ∤ N ((p ² - 3 p + 3) / p ²)$ . Let ε > 0 be arbitrary and $R = N^{1 / 8 - ε}$ . We prove that for all positive integers r ≤ R, with at most $O (R l o g^{- A} N)$ exceptions, the Diophantine equation ⎧N = p₁+p₂+p₃, ⎨ $p_{j} \equiv b_{j} (m o d r),$ 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

J. F. Koksma (1964)

Compositio Mathematica

The Theta Correspondence and Harmonic Forms. I.

Stephen S. Kudla, John J. Millson (1986)

Mathematische Annalen

The Theta Correspondence and Harmonic Forms. II.

Stephen S. Kudla, John J. Milson (1987)

Mathematische Annalen

The three-dimensional Gauss algorithm is strongly convergent almost everywhere.

Hardcastle, D.M. (2002)

Experimental Mathematics

The topological structure of the set of subsums of an infinite series

J. A. Guthrie, J. E. Nymann (1988)

Colloquium Mathematicae

The topology of rational points.

Mazur, Barry (1992)

Experimental Mathematics

The torsion elements in K₂ of some local fields

Xuejun Guo (2007)

Acta Arithmetica

The torsion subgroup of a family of elliptic curves over the maximal abelian extension of $ℚ$

Jerome Tomagan Dimabayao (2020)

Czechoslovak Mathematical Journal

We determine explicitly the structure of the torsion group over the maximal abelian extension of $ℚ$ and over the maximal $p$ -cyclotomic extensions of $ℚ$ for the family of rational elliptic curves given by $y^{2} = x^{3} + B$ , where $B$ is an integer.

Currently displaying 941 – 960 of 1341

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Displaying 941 – 960 of 1341

The Tate pairing for Abelian varieties over finite fields

The tensor product of exceptional representations on the general linear group

The terms $C x^{h} (h \geq 3)$ 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

The ternary Goldbach problem.

The ternary Goldbach problem in arithmetic progressions

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 $ℚ$

The totally real $A_{5}$ extension of degree 6 with minimum discriminant.

The totally real $A_{6}$ 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.

Currently displaying 941 – 960 of 1341