Counting integer points on affine surfaces with a side condition
Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12.
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Abstract
We extend work of Heath-Brown and Salberger, based on the determinant method, to provide a uniform upper bound for the number of integral points of bounded height on an affine surface, which are subject to a polynomial congruence condition. This is applied to get a new uniform bound for points on diagonal quadric surfaces, and to a problem about the representation of integers as a sum of four unlike powers.
Publishing Year
Date Published
2025-09-01
Journal Title
Discrete Analysis
Publisher
Cambridge: Alliance of Diamond Open Access Journals
Acknowledgement
Supported by FWF grant (DOI 10.55776/P36278), Supported by European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant
Agreement No. 101034413.
Volume
2025
Article Number
12
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IST-REx-ID
Cite this
Browning TD, Verzobio M. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025;2025. doi:10.19086/da.143787
Browning, T. D., & Verzobio, M. (2025). Counting integer points on affine surfaces with a side condition. Discrete Analysis. Cambridge: Alliance of Diamond Open Access Journals. https://doi.org/10.19086/da.143787
Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” Discrete Analysis. Cambridge: Alliance of Diamond Open Access Journals, 2025. https://doi.org/10.19086/da.143787.
T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces with a side condition,” Discrete Analysis, vol. 2025. Cambridge: Alliance of Diamond Open Access Journals, 2025.
Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12.
Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” Discrete Analysis, vol. 2025, 12, Cambridge: Alliance of Diamond Open Access Journals, 2025, doi:10.19086/da.143787.
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