Gaps in sumsets of $s$ pseudo s-th power sequences
Number Theory
2014-05-07 v2 Combinatorics
Abstract
We study the length of the gaps between consecutive members in the sumset sA when A is a pseudo s-th power sequence, with s>1. We show that, almost surely, limsup (b_{n+1}-b_{n})/log (b_n) = s^s s!/\Gamma^s(1/s), where b_n are the elements of sA.
Cite
@article{arxiv.1404.5237,
title = {Gaps in sumsets of $s$ pseudo s-th power sequences},
author = {Javier Cilleruelo and Jean-Marc Deshouillers},
journal= {arXiv preprint arXiv:1404.5237},
year = {2014}
}
Comments
Corrected a mistake in Lemma 1