On a paper of Erdös and Szekeres

Abstract

Propositions 1.1 -- 1.3 stated below contribute to results and certain problems considered in a paper by Erdos and Szekeres, on the behavior of products ${\prod }_1^n(1-z^{a_j}),1\le a_1\le \cdots \le a_n$ integers. In the discussion, $\{a_1,\dots ,a_n\}$ will be either a proportional subset of $\{1,\dots ,n\}$ or a set of large arithmetic diameter.