5 papers
Fermat near misses and the integral Hilbert Property
Jessica Alessandrì, Daniel Loughran
We consider the Diophantine equation for , which is related to near misses for the quartic case of Fermat's Last Theorem. For certain we…
Lower bounds for counting -quartic fields
Daniel Loughran, Ross Paterson
A conjecture of Malle predicts the quantity of number fields with bounded discriminant of given Galois group. We present a lower bound matching this in the case of quartic fields w…
Rational points in a family of conics over
Daniel Loughran, Judith Ortmann
Serre famously showed that almost all plane conics over have no rational point. We investigate versions of this over global function fields, focusing on a specific fam…
Rationality and arithmetic of the moduli of abelian varieties
Daniel Loughran, Gregory Sankaran
We study the rationality properties of the moduli space of principally polarised abelian -folds over and apply the results to arithmetic questions.…
An Erdős-Kac law for local solubility in families of varieties
Daniel Loughran, Efthymios Sofos
We study probability distributions arising from local obstructions to the existence of -adic points in families of varieties. In certain cases we show that an Erdős-Kac type law…