Additive properties of sequences of pseudo $s$-th powers
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en
Article de revue
Este ítem está publicado en
Mathematische Zeitschrift. 2016, vol. 284, p. 175-193
Springer
Resumen en inglés
In this paper, we study (random) sequences of pseudo s-th powers, as introduced by Erdös and Rényi in 1960. In 1975, Goguel proved that such a sequence is almost surely not an asymptotic basis of order s. Our first result ...Leer más >
In this paper, we study (random) sequences of pseudo s-th powers, as introduced by Erdös and Rényi in 1960. In 1975, Goguel proved that such a sequence is almost surely not an asymptotic basis of order s. Our first result asserts that it is however almost surely a basis of order s + x for any x > 0. We then study the s-fold sumset sA = A + ... + A (s times) and in particular the minimal size of an additive complement, that is a set B such that sA + B contains all large enough integers. With respect to this problem, we prove quite precise theorems which are tantamount to asserting that a threshold phenomenon occurs.< Leer menos
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