Writing integers as sums of products

Abstract

In this paper we obtain an asymptotic expression for the number of ways of writing an integer N as a sum of k products of l factors, valid for k ≥ 3 k \geq 3 and l ≥ 2 l \geq 2 . The proof is an application of the Hardy-Littlewood method, and uses recent results from the divisor problem for arithmetic progressions.