Abstract
We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over ℝ and over ℚp for all primes p, provided that the form
has at least (d - d1/2/2)2d variables.
This improves on a longstanding result of Birch.
Original language | English |
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Pages (from-to) | 203-234 |
Number of pages | 32 |
Journal | Journal für die reine und angewandte Mathematik |
Volume | 2017 |
Issue number | 731 |
Early online date | 20 Feb 2015 |
DOIs | |
Publication status | Published - 1 Oct 2017 |
Keywords
- math.NT
- 11P55 (11G35, 14G05)