Estimates are provided for sth moments of cubic smooth Weyl sums, when 4 ≤ s ≤ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-1-6,
author = {Trevor D. Wooley},
title = {Sums of three cubes, II},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {73-100},
zbl = {06459959},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-1-6}
}
Trevor D. Wooley. Sums of three cubes, II. Acta Arithmetica, Tome 168 (2015) pp. 73-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-1-6/