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Additive bases in groups

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Abstract

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 ℕ) 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 G.

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Authors and Affiliations

  1. Centre de Mathématiques Laurent Schwartz, École polytechnique, 91128, Palaiseau Cedex, France

    Victor Lambert, Thái Hoàng Lê & Alain Plagne

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  1. Victor Lambert
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  2. Thái Hoàng Lê
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  3. Alain Plagne
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Correspondence to Alain Plagne.

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Lambert, V., Lê, T.H. & Plagne, A. Additive bases in groups. Isr. J. Math. 217, 383–411 (2017). https://doi.org/10.1007/s11856-017-1452-8

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  • DOI: https://doi.org/10.1007/s11856-017-1452-8

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