Sums of three cubes, II

Abstract

Estimates are provided for $s$th moments of cubic smooth Weyl sums, when $4\le s\le 8$, by enhancing the author's iterative method that delivers estimates beyond classical convexity. As a consequence, an improved lower bound is presented for the number of integers not exceeding $X$ that are represented as the sum of three cubes of natural numbers.

25 pages

References in corpus (2)

• Correlation estimates for sums of three cubes
• The Hasse principle for systems of diagonal cubic forms