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arXiv · 2408.11453

Counting integer points on affine surfaces with a side condition

Tim Browning·Matteo Verzobio
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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.

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Tim Browning, Matteo Verzobio. 2024-08-21. Counting integer points on affine surfaces with a side condition. https://doi.org/10.19086/da.143787

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