Random diophantine equations of large degree
Browning TD, Sawin W. 2026. Random diophantine equations of large degree. The Quarterly Journal of Mathematics., haag037.
Download (ext.)
Journal Article
| Epub ahead of print
| English
Scopus indexed
Author
Browning, Timothy DISTA 
;
Sawin, Will
;
Sawin, WillCorresponding author has ISTA affiliation
Department
Abstract
Among the set of hypersurfaces of degree d and dimension defined by the vanishing
of a homogeneous polynomial with coefficients in the set {−1, +1}, we investigate the
probability that a hypersurface contains a rational point as d and tend to ∞.
Publishing Year
Date Published
2026-10-06
Journal Title
The Quarterly Journal of Mathematics
Publisher
Oxford University Press
Acknowledgement
The authors are very grateful to Pierre Le Boudec, whose contributions would have merited coauthorship. At his request, however, he is not listed as a co-author, since he has chosen to pursue
a career outside academia. T.B. was supported by a grant from the IAS School of Mathematics
and a FWF grant (DOI 10.55776/P36278). W.S. was supported by NSF grant DMS-2502029 and
a Sloan Research Fellowship.
Article Number
haag037
ISSN
eISSN
IST-REx-ID
Cite this
Browning TD, Sawin W. Random diophantine equations of large degree. The Quarterly Journal of Mathematics. 2026. doi:10.1093/qmath/haag037
Browning, T. D., & Sawin, W. (2026). Random diophantine equations of large degree. The Quarterly Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haag037
Browning, Timothy D, and Will Sawin. “Random Diophantine Equations of Large Degree.” The Quarterly Journal of Mathematics. Oxford University Press, 2026. https://doi.org/10.1093/qmath/haag037.
T. D. Browning and W. Sawin, “Random diophantine equations of large degree,” The Quarterly Journal of Mathematics. Oxford University Press, 2026.
Browning TD, Sawin W. 2026. Random diophantine equations of large degree. The Quarterly Journal of Mathematics., haag037.
Browning, Timothy D., and Will Sawin. “Random Diophantine Equations of Large Degree.” The Quarterly Journal of Mathematics, haag037, Oxford University Press, 2026, doi:10.1093/qmath/haag037.
All files available under the following license(s):
Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):
Link(s) to Main File(s)
Access Level
Open Access
arXiv 
Google Scholar