30 citations · 73 across the 25 of their papers we have counts for
6 papers · 1 filter
Elementary methods for incidence problems in finite fields
Javier Cilleruelo, Alex Iosevich, Ben Lund +2
We use elementary methods to prove an incidence theorem for points and spheres in . As an application, we show that any point set of with…
Additive properties of sequences of pseudo s-th powers
Javier Cilleruelo, Jean-Marc Deshouillers, Victor Lambert +1
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 asym…
Gaps in sumsets of pseudo s-th power sequences
Javier Cilleruelo, Jean-Marc Deshouillers
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})/l…
A note on product sets of rationals
Javier Cilleruelo
Bourgain, Konyagin and Shparlinski obtained a lower bound for the size of the product set AB when A and B are sets of positive rational numbers with numerator and denominator less…
Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications
J. Cilleruelo, M. Z. Garaev
In the present paper we obtain new upper bound estimates for the number of solutions of the congruence $$ x\equiv y r\pmod p;\quad x,y\in \mathbb{N},\quad x,y\le H,\quad r\in\cU, $…
Infinite graphs that do not contain cycles of length four
Javier Cilleruelo
We construct a countable infinite graph G that does not contain cycles of length four having the property that the sequence of graphs induced by the first vertices has mi…