Weyl's inequality and systems of forms
Number Theory
2014-04-08 v2
Abstract
By providing a variant of Weyl's inequality for general systems of forms we establish the Hardy-Littlewood asymptotic formula for the density of integer zeros of systems of quadratic or cubics forms under weaker rank conditions than previously known. We also briefly discuss what happens for systems of higher degree forms, and slightly relax the non-singularity condition in Birch's paper on forms in many variables.
Cite
@article{arxiv.1208.1968,
title = {Weyl's inequality and systems of forms},
author = {Rainer Dietmann},
journal= {arXiv preprint arXiv:1208.1968},
year = {2014}
}
Comments
version 2; 12 pages; submitted for publication (in revised form resubmitted 19th March 2014); reference added to a recent preprint containing independent work on this by Damaris Schindler