Daniel Loughran

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20172025

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math.NT2025

Fermat near misses and the integral Hilbert Property

Jessica Alessandrì, Daniel Loughran

We consider the Diophantine equation $x^{4} + y^{4} - w^{2} = n$ for $n \in Z$ , which is related to near misses for the quartic case of Fermat's Last Theorem. For certain $n$ we…

math.NT2025

Lower bounds for counting $A_{4}$ -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…

math.NT2024

Rational points in a family of conics over $F_{2} (t)$

Daniel Loughran, Judith Ortmann

Serre famously showed that almost all plane conics over $Q$ have no rational point. We investigate versions of this over global function fields, focusing on a specific fam…

math.NT2017

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 $p$ -adic points in families of varieties. In certain cases we show that an Erdős-Kac type law…

Fermat near misses and the integral Hilbert Property

Lower bounds for counting A4​-quartic fields

Rational points in a family of conics over F2​(t)

An Erdős-Kac law for local solubility in families of varieties

Lower bounds for counting $A_{4}$ -quartic fields

Rational points in a family of conics over $F_{2} (t)$