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arXiv · 1402.4489

Improvements in Birch's theorem on forms in many variables

T. D. Browning·Sean Prendiville
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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.

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T. D. Browning, Sean Prendiville. 2014-02-18. Improvements in Birch's theorem on forms in many variables. https://arxiv.org/abs/1402.4489

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