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Conjecture de Littlewood et récurrences linéaires

Bernard de Mathan (2003)

Journal de théorie des nombres de Bordeaux

Ce travail est essentiellement consacré à la construction d’exemples effectifs de couples ( α , β ) de nombres réels à constantes de Markov finies, tels que 1 , α et β soient 𝐙 -linéairement indépendants, et satisfaisant à la conjecture de Littlewood.

Counting rational points near planar curves

Ayla Gafni (2014)

Acta Arithmetica

We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².

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