Arithmetic properties of thin sets (Q1082563)

We study arithmetic properties of \(\Lambda\) (p) sets for \(p>0\), and in particular show that \(\Lambda\) (p) sets do not contain parallelepipeds of arbitrarily large dimension. From this it follows that all \(\Lambda\) (p) sets satisfy the arithmetic properties which were previously known only for \(\Lambda\) (p) sets with \(p>2\). Random sequences are considered to show that parallelepipeds are not sufficient to characterize \(\Lambda\) (4) sets.