𝑝-Rider sets are 𝑞-Sidon sets

Abstract

The aim of this paper is to prove that for every p > 4 3 p>{\frac 43} , every p p -Rider set is a q q -Sidon set for all q > p 2 − p ⋅ q>{\frac p{2-p}}\cdot This gives some positive answers for the union problem of p p -Sidon sets. We also obtain some results on the behavior of the Fourier coefficient of a measure with spectrum in a p p -Rider set.