Daniel Loughran

collaborators

3 papers

math.NT2025

Fermat near misses and the integral Hilbert Property

Jessica AlessandrÃ¬, 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.NT2025

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…

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)

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

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