Tim Browning

activity

20242026

most citedSums of three cubes over a function field

1 citations · 2 across the 6 of their papers we have counts for

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8 papers · 1 filter

math.NT2026

Counting matrices with given characteristic polynomial

Tim Browning, Fabian Gundlach, Will Sawin

Let $f$ be a monic polynomial of degree $n$ with integer coefficients. We use Fourier analysis to prove a new upper bound on the number of $n \times n$ matrices with characteristic…

math.NT2026

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…

math.NT2026

The divisor function for matrices

Tim Browning, Nikita P. Kalinin, Alina Ostafe +2

We introduce a matrix divisor function $τ_{n} (T, M)$ , counting factorisations $A B = M$ for $n \times n$ integer matrices $A, B$ of height at most $T$ . For a fixed non-singular $M$ , or for…

math.NT2026

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.

math.NT2025

Random Diophantine equations of large degree

Tim Browning, Will Sawin

Among the set of hypersurfaces of degree $d$ and dimension $ℓ$ defined by the vanishing of a homogeneous polynomial with coefficients $\pm 1$ , we investigate the probability tha…

math.NT2024

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 $n \times n$ matrices with integer entries in $[- T, T]$ , as $T \to \infty$ . Our work uses Fourier analysis and lead…

math.NT2024★ 1 cited

Optimal sums of three cubes in $F_{q} [t]$

Tim Browning, Jakob Glas, Victor Y. Wang

We use the circle method to prove that a density 1 of elements in $F_{q} [t]$ are representable as a sum of three cubes of essentially minimal degree from $F_{q} [t]$ ,…

math.NT2024★ 1 cited

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 $F_{q} [t]$ are representable as a sum of three cubes of minimal degre…

Counting matrices with given characteristic polynomial

The Artin-Davenport conjecture on cubic forms

The divisor function for matrices

Beyond the square-root barrier: cubic forms of Perazzo type

Random Diophantine equations of large degree

Pairs of commuting integer matrices

Optimal sums of three cubes in Fq​[t]

Sums of three cubes over a function field

Optimal sums of three cubes in $F_{q} [t]$