24 citations · 171 across the 47 of their papers we have counts for
57 papers
Square-free values of random polynomials
Tim Browning, Igor Shparlinski
The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We…
A motivic circle method
Margaret Bilu, Tim Browning
The circle method has been successfully used over the last century to study rational points on hypersurfaces. More recently, a version of the method over function fields, combined…
Generalised quadratic forms over totally real number fields
Tim Browning, Lillian B. Pierce, Damaris Schindler
We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the ra…
Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
Tim Browning, Efthymios Sofos, Joni Teräväinen
With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree d polynomials f that are ordered by height. This allows us to establish…
Density of rational points on some quadric bundle threefolds
Dante Bonolis, Tim Browning, Zhizhong Huang
We prove the Manin-Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1,2). The proof uses a…
Local solubility for a family of quadrics over a split quadric surface
Tim Browning, Julian Lyczak, Roman Sarapin
We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface.