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math.NT2026
Sums of three powerful numbers
Tim Browning, Matteo Verzobio
Let and consider the Campana orbifold \[ \left( \mathbb{P}^1, \left(1-\tfrac1p\right)[0] +\left(1-\tfrac1q\right)[1] +\left(1-\tfrac1r\right)[\infty] \right). \] Prim…
math.NT2025
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…