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math.NT2019
Brauer-Manin obstruction for Erdős-Straus surfaces
Martin Bright, Daniel Loughran
We study the failure of the integral Hasse principle and strong approximation for the Erdős-Straus conjecture using the Brauer-Manin obstruction.
math.NT2019
Rank jumps on elliptic surfaces and the Hilbert property
Daniel Loughran, Cecília Salgado
Given an elliptic surface over a number field, we study the collection of fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable assumptions, we show that…
math.NT2017
Sieving rational points on varieties
Tim Browning, Daniel Loughran
A sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, the number of varieties in a family which are e…