Ross Paterson

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20232025

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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…