Improvements in Birch's theorem on forms in many variables
Number Theory
2014-02-20 v1
Abstract
We show that a non-singular integral form of degree d is soluble non-trivially over the integers if and only if it is soluble non-trivially over the reals and the p-adic numbers, provided that the form has at least (d-\sqrt{d}/2)2^d variables. This improves on a longstanding result of Birch.
Keywords
Cite
@article{arxiv.1402.4489,
title = {Improvements in Birch's theorem on forms in many variables},
author = {T. D. Browning and Sean Prendiville},
journal= {arXiv preprint arXiv:1402.4489},
year = {2014}
}
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36 pages