1 citations · 2 across the 6 of their papers we have counts for
4 papers · 1 filter
Counting matrices with given characteristic polynomial
Tim Browning, Fabian Gundlach, Will Sawin
Let be a monic polynomial of degree with integer coefficients. We use Fourier analysis to prove a new upper bound on the number of matrices with characteristic…
The Artin-Davenport conjecture on cubic forms
Dante Bonolis, Tim Browning, Jakob Glas +1
We show that any integral cubic form in ten or more variables has a nontrivial integer zero. Like earlier authors on this topic, we use geometric methods to produce a zero in some…
The divisor function for matrices
Tim Browning, Nikita P. Kalinin, Alina Ostafe +2
We introduce a matrix divisor function , counting factorisations for integer matrices of height at most . For a fixed non-singular , or for…
Beyond the square-root barrier: cubic forms of Perazzo type
Tim Browning, Ritabrata Munshi, Victor Y. Wang
We show how the circle method can be used to study rational points on a certain cubic fourfold, going beyond the square-root barrier.