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math.NT2026
Towards linear growth for biprojective hypersurfaces of small dimension
Tim Browning, Matteo Verzobio
After removing suitable thin subsets, we count rational points of bounded height on some hypersurfaces of small bidegree in and in $\mathbb{P}^3\ti…
math.NT2024
Counting integer points on affine surfaces with a side condition
Tim Browning, Matteo Verzobio
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 surf…
math.NT2024
Integral points on cubic surfaces: heuristics and numerics
Tim Browning, Florian Wilsch
We develop a heuristic for the density of integer points on affine cubic surfaces. Our heuristic applies to smooth surfaces defined by cubic polynomials that are log K3, but it can…