Integral solutions to systems of diagonal equations
Number Theory
2025-11-05 v2
Abstract
In this paper, we obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We improve the required number of variables compared to previous results by incorporating the recent progress on Waring's problem and the resolution of the main conjecture in Vinogradov's mean value theorem.
Cite
@article{arxiv.2406.09256,
title = {Integral solutions to systems of diagonal equations},
author = {Nick Rome and Shuntaro Yamagishi},
journal= {arXiv preprint arXiv:2406.09256},
year = {2025}
}
Comments
Significant updates to fill in gaps and bring results more in line with the state of the art in Waring's problem