Sur le nombre d'éléments exceptionnels d'une base additive
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Alain Plagne
Abstract
In a paper recently published in Crelle's Journal, Deschamps and Grekos [B. Deschamps et G. Grekos, Estimation du nombre d'exceptions à ce qu'un ensemble de base privé d'un point reste un ensemble de base, J. reine angew. Math. 539 (2001), 45–53.] study asymptotically (when h tends to infinity) the quantity E(h), introduced by Erdős and Graham, and defined as the maximal number of elements which are necessary to the basicity of an additive basis of order h. They show that the maximal order of this function is (h/log h)½. The aim of this article is to show that the E function does not have oscillations but, to the contrary, does possess a regular asymptotic behaviour, that we determine explicitly. More precisely, we prove that E(h) ~ 2(h/log h)½.
© Walter de Gruyter
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Articles in the same Issue
- Smooth localized parametric resonance for wave equations
- Estimates and regularity results for the DiPerna-Lions flow
- Sur le nombre d'éléments exceptionnels d'une base additive
- Alder's conjecture
- Local monotonicity and mean value formulas for evolving Riemannian manifolds
- Projective-injective modules, Serre functors and symmetric algebras
- Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
- Zeros of complex caloric functions and singularities of complex viscous Burgers equation
- Generalised form of a conjecture of Jacquet and a local consequence
