Ross Paterson

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20232025

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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

Local solubility of generalised Fermat equations

Peter Koymans, Ross Paterson, Tim Santens +1

For every $n \geq 2$ we determine the asymptotic formula for the number of integer triples $(a, b, c)$ of bounded absolute value such that the generalised Fermat equation given by $a…

math.NT2024

Quadratic Twists as Random Variables

Ross Paterson

Let $D \neq = 1$ be a fixed squarefree integer. For elliptic curves $E / Q$ , writing $E_{D}$ for the quadratic twist by $D$ , we consider the question of how often $E (Q)$ …

math.NT2024

2-Selmer Groups over Multiquadratic Extensions

Ross Paterson

Let K be a multiquadratic number field. We investigate the average dimension of 2-Selmer groups over K for the family of all elliptic curves over the rational numbers (ordered by h…

math.NT2023

Conductors of twisted Weil--Deligne representations

Matthew Bisatt, Ross Paterson

We study the behaviour of conductors of L-functions associated to certain Weil--Deligne representations under twisting. For each global field K we prove a sharp upper bound for the…

Lower bounds for counting A4​-quartic fields

Local solubility of generalised Fermat equations

Quadratic Twists as Random Variables

2-Selmer Groups over Multiquadratic Extensions

Conductors of twisted Weil--Deligne representations

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