A large gap in a dilate of a set

2020/04/29 by Shakan, George
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.14828

Abstract

Let A ⊂ \mathbbF_p with |A| > 1. We show there is a d ∈ \mathbbF_p^× such that d ⋅ A contains a gap of size at least 2p/ |A| - 2 .

Related

• On the maximal volume of empty convex bodies amidst multivariate dilates of a lacunary integer sequence
• Bounds on the gaps in the fractional parts of a linear form
• Large gaps between sums of two squares
• Sums of dilates in ℤ_p
• Gap Theorem for Separated Sequences without Pain