24 citations · 171 across the 47 of their papers we have counts for
5 papers · 1 filter
Square-free values of reducible polynomials
Andrew Booker, Tim Browning
We calculate admissible values of r such that a square-free polynomial with integer coefficients, no fixed prime divisor and irreducible factors of degree at most 3 takes infinitel…
A transference approach to a Roth-type theorem in the squares
Tim Browning, Sean Prendiville
We show that any subset of the squares of positive relative upper density contains non-trivial solutions to a translation-invariant linear equation in five or more variables, with…
Strong approximation and a conjecture of Harpaz and Wittenberg
Tim Browning, Damaris Schindler
We study strong approximation for some algebraic varieties over which are defined using norm forms over the rationals. This allows us to confirm a special case of a conjecture due…
Rational points on cubic hypersurfaces over
Tim Browning, Pankaj Vishe
For any finite field k of characteristic exceeding 3, the Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field k(t),…
Rational curves on smooth cubic hypersurfaces over finite fields
Tim Browning, Pankaj Vishe
Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least…