Earlier Version
Improvements in Birch's theorem on forms in many variables
Browning TD, Prendiville S. Improvements in Birch’s theorem on forms in many variables. Journal fur die Reine und Angewandte Mathematik. 2017(731), 203–234.
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Author
Browning, Timothy DISTA 
;
Prendiville, Sean
;
Prendiville, SeanAbstract
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.
Publishing Year
Date Published
2015-02-20
Journal Title
Journal fur die Reine und Angewandte Mathematik
Acknowledgement
While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.
Volume
2017
Issue
731
Page
203 - 234
ISSN
IST-REx-ID
Cite this
Browning TD, Prendiville S. Improvements in Birch’s theorem on forms in many variables. Journal fur die Reine und Angewandte Mathematik. 2017(731):203-234. doi:10.1515/crelle-2014-0122
Browning, T. D., & Prendiville, S. (n.d.). Improvements in Birch’s theorem on forms in many variables. Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter. https://doi.org/10.1515/crelle-2014-0122
Browning, Timothy D, and Sean Prendiville. “Improvements in Birch’s Theorem on Forms in Many Variables.” Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter, n.d. https://doi.org/10.1515/crelle-2014-0122.
T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms in many variables,” Journal fur die Reine und Angewandte Mathematik, vol. 2017, no. 731. Walter de Gruyter, pp. 203–234.
Browning TD, Prendiville S. Improvements in Birch’s theorem on forms in many variables. Journal fur die Reine und Angewandte Mathematik. 2017(731), 203–234.
Browning, Timothy D., and Sean Prendiville. “Improvements in Birch’s Theorem on Forms in Many Variables.” Journal Fur Die Reine Und Angewandte Mathematik, vol. 2017, no. 731, Walter de Gruyter, pp. 203–34, doi:10.1515/crelle-2014-0122.
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