24 citations · 171 across the 47 of their papers we have counts for
51 papers · 1 filter
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…
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.
Equidistribution and freeness on Grassmannians
Tim Browning, Tal Horesh, Florian Wilsch
We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians an…