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arXiv · 1508.02662

Additive bases in groups

Victor Lambert·Thái Hoàng Lê·Alain Plagne
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Abstract

In this paper, we study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions $X$, $S$ and $E$ (defined in the case of the integers) and obtain bounds on them. Our estimates on the functions $S_G$ and $E_G$ are valid for general abelian groups $G$ while in the case of $X_G$ we show that distinct types of behaviours may occur depending on the group $G$.

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Victor Lambert, Thái Hoàng Lê, Alain Plagne. 2015-08-11. Additive bases in groups. https://arxiv.org/abs/1508.02662

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