17 citations · 64 across the 22 of their papers we have counts for
4 papers · 1 filter
Quantitative arithmetic of diagonal degree K3 surfaces
Damián Gvirtz-Chen, Daniel Loughran, Masahiro Nakahara
In this paper we study the existence of rational points for the family of K3 surfaces over given by When the coefficients are…
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.
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…
Frobenian multiplicative functions and rational points in fibrations
Daniel Loughran, Lilian Matthiesen
We consider the problem of counting the number of varieties in a family over with a rational point. We obtain lower bounds for this counting problem for some families…