Sums of dilates in $\mathbb{Z}_p$

Details Sums of dilates in $\mathbb{Z}_p$ Sums of dilates in $\mathbb{Z}_p$

2012-03-12

arxiv.org/abs/1203.2659v2

Mathematics

Combinatorics

Scientific paper

We consider the problem of sums of dilates in groups of prime order. We show that given $A\subset \Z{p}$ of sufficiently small density then $$\big| \lambda_{1}A+\lambda_{2}A+...+ \lambda_{k}A \big| \,\ge\,\bigg(\sum_{i}|\lambda_{i}|\bigg)|A|- o(|A|),$$ whereas on the other hand, for any $\epsilon>0$, we construct subsets of density $1/2-\epsilon$ such that $|A+\lambda A|\leq (1-\delta)p$, showing that there is a very different behaviour for subsets of large density.

Affiliated with

Also associated with

No associations

Rating

Sums of dilates in $\mathbb{Z}_p$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sums of dilates in $\mathbb{Z}_p$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sums of dilates in $\mathbb{Z}_p$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-143192