On the number of exceptional elements of an additive basis. (Sur le nombre d’éléments exceptionnels d’une base additive.) (French) Zbl 1221.11201
In [J. Reine Angew. Math. 539, 45–53 (2001; Zbl 1002.11011)] B. Deschamps and G. Grekos studied 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 showed that the maximal order of this function is \((h/\log h)^{1/2}\).
Here the authors show that \(E\) does not have oscillations but, to the contrary, possesses a regular asymptotic behaviour, that is determined explicitly. More precisely, they prove that \(E(h)\sim 2(h/\log h)^{1/2}\).
Here the authors show that \(E\) does not have oscillations but, to the contrary, possesses a regular asymptotic behaviour, that is determined explicitly. More precisely, they prove that \(E(h)\sim 2(h/\log h)^{1/2}\).
Reviewer: Olaf Ninnemann (Berlin)
Citations:
Zbl 1002.11011References:
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