1 citations · 3 across the 5 of their papers we have counts for
5 papers · 1 filter
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…
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.
Pairs of commuting integer matrices
Tim Browning, Will Sawin, Victor Y. Wang
We prove upper and lower bounds on the number of pairs of commuting matrices with integer entries in , as . Our work uses Fourier analysis and lead…
Optimal sums of three cubes in
Tim Browning, Jakob Glas, Victor Y. Wang
We use the circle method to prove that a density 1 of elements in are representable as a sum of three cubes of essentially minimal degree from ,…
Sums of three cubes over a function field
Tim Browning, Jakob Glas, Victor Y. Wang
We use a function field version of the circle method to prove that a positive proportion of elements in are representable as a sum of three cubes of minimal degre…