Rydin Myerson, SL;
(2019)
Systems of cubic forms in many variables.
Journal für die reine und angewandte Mathematik
, 2019
(757)
pp. 309-328.
10.1515/crelle-2017-0040.
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Abstract
We consider a system of R cubic forms in n variables, with integer coefficients, which define a smooth complete intersection in projective space. Provided n≥25R, we prove an asymptotic formula for the number of integer points in an expanding box at which these forms simultaneously vanish. In particular, we obtain the Hasse principle for systems of cubic forms in 25R variables, previous work having required that n≫R2. One conjectures that n≥6R+1 should be sufficient. We reduce the problem to an upper bound for the number of solutions to a certain auxiliary inequality. To prove this bound we adapt a method of Davenport.
| Type: | Article |
|---|---|
| Title: | Systems of cubic forms in many variables |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/crelle-2017-0040 |
| Publisher version: | https://doi.org/10.1515/crelle-2017-0040 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10025899 |
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