An Erdős--Fuchs Theorem for Ordered Representation Functions

Gonzalo Cao-Labora, Juanjo Rué, Christoph Spiegel

Let $k\ge 2$ be a positive integer. We study concentration results for the ordered representation functions $r^{\leq}_k(A,n) = \# \big\{ (a_1 \leq \dots \leq a_k) \in A^k : a_1+\d…