Rational points on an intersection of diagonal forms
Volume 203 / 2022
Acta Arithmetica 203 (2022), 165-194
MSC: Primary 11P55, 11L15; Secondary 11L07.
DOI: 10.4064/aa210310-18-12
Published online: 11 April 2022
Abstract
We consider intersections of $n$ diagonal forms of degrees $k_1 \lt \cdots \lt k_n$, and we prove an asymptotic formula for the number of rational points of bounded height on these varieties. The proof uses the Hardy–Littlewood method and recent breakthroughs on the Vinogradov system. We also give a sharper result for one specific value of $(k_1,\ldots ,k_n)$, using a technique due to Wooley and an estimate on exponential sums derived from a recent approach in the van der Corput method.
