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math.NT2025
Counting rational points on smooth hypersurfaces with high degree
Matteo Verzobio
Let be a smooth projective hypersurface defined over . We provide new bounds for rational points of bounded height on . In particular, we show that if is a s…
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
Strong divisibility sequences and sieve methods
Tim Browning, Matteo Verzobio
We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence which only have (somewhat) large prime factors. We focus…