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We consider Thue equations of the form $a x^{k} + b y^{k} = 1$ , and assuming the truth of the abc-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle. A similar conclusion holds true for Fermat equations $a x^{k} + b y^{k} + c z^{k} = 0$ of degree at least six.

Random walks on infinite self-similar graphs.

Neunhäuserer, Jörg (2007)

Electronic Journal of Probability [electronic only]

Rang de courbes elliptiques avec groupe de torsion non trivial

Odile Lecacheux (2003)

Journal de théorie des nombres de Bordeaux

On construit des courbes elliptiques sur $ℚ (T)$ de rang au moins 3, avec un sous-groupe de torsion non trivial. Par spécialisation, des courbes elliptiques de rang 5 et 6 sur $ℚ$ sont obtenues.

Rang des courbes elliptiques et sommes d'exponentielles.

Etienne Fouvry, Jacek Pomykala (1993)

Monatshefte für Mathematik

Rang moyen de familles de courbes elliptiques et lois de Sato-Tate.

Philippe Michel (1995)

Monatshefte für Mathematik

Rang $p$ -adique du groupe des unités d’un corps de nombres

Jean Fresnel (1968/1969)

Séminaire de théorie des nombres de Bordeaux

Rang p-adique d'unités et action de groupes.

Michel Laurent (1989)

Journal für die reine und angewandte Mathematik

Range of density measures

Martin Sleziak, Miloš Ziman (2009)

Acta Mathematica Universitatis Ostraviensis

We investigate some properties of density measures – finitely additive measures on the set of natural numbers $ℕ$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence $(\frac{A (n)}{n})$ as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of $ℕ$ . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...

Rank $1$ forms, closed zones and laminae

Michel Deza, Viatcheslav Grishukhin (2002)

Journal de théorie des nombres de Bordeaux

For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank $1$ quadratic forms which are extreme rays for the corresponding $L$ -type domain.

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Displaying 41 – 60 of 548

Ramsey problems in additive number theory

Random $B_{h}$ sets and additive bases in $ℤ_{n}$ .

Random fields on the adele ring and Wilson's renormalization group

Random generators and normal numbers.

Random Liouville functions and normal sets

Random matrices, magic squares and matching polynomials.

Random matrix theory and the Fourier coefficients of half-integral weight forms.

Random Sums Related To Prime Divisors Of An Integer

Random Thue and Fermat equations