32 citations · 131 across the 18 of their papers we have counts for
18 papers
Many cubic surfaces contain rational points
T. D. Browning
Building on recent work of Bhargava--Elkies--Schnidman and Kriz--Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain ration…
Counting rational points on quartic del Pezzo surfaces with a rational conic
T. D. Browning, E. Sofos
Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over that…
Power-free values of polynomials on symmetric varieties
T. D. Browning, A. Gorodnik
Given a symmetric variety Y defined over the rationals and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions unde…
Failures of weak approximation in families
M. Bright, T. D. Browning, D. Loughran
Given a family of varieties over a number field , we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for o…
Counting rational points on del Pezzo surfaces with a conic bundle structure
T. D. Browning, M. Swarbrick Jones
For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped wit…
Varieties with too many rational points
T. D. Browning, D. Loughran
We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the varie…