T. Weston

activity

20242026

collaborators

Showing math.NTShow all

6 papers · 1 filter

math.NT2026

Dedekind zeta functions of non-Galois torsion fields of elliptic curves

Robert Pollack, Tom Weston

We give an algorithm to determine factorization types of primes in the number fields generated by a single point of odd order on an elliptic curve. We apply this to compute coeffic…

math.NT2025

Diophantine stability for elliptic curves on average

Anwesh Ray, Tom Weston

Let $K$ be a number field and $ℓ \geq 5$ a prime number. Mazur and Rubin introduced the notion of diophantine stability for a variety $X_{/ K}$ at a prime $ℓ$ . We show that th…

math.NT2024

Explicit reciprocity laws and Iwasawa theory for modular forms

Matthew Emerton, Robert Pollack, Tom Weston

We prove that the Mazur-Tate elements of an eigenform $f$ sit inside the Fitting ideals of the corresponding dual Selmer groups along the cyclotomic $Z_{p}$ -extension (up to…

math.NT2024

Class group statistics for torsion fields generated by elliptic curves

Anwesh Ray, Tom Weston

For a prime $p$ and a rational elliptic curve $E_{/ Q}$ , set $K = Q (E [p])$ to denote the torsion field generated by $E [p] := ker {E p E}$ .…

math.NT2024

Hilbert's tenth problem in Anticyclotomic towers of number fields

Anwesh Ray, Tom Weston

Let $K$ be an imaginary quadratic field and $p$ be an odd prime which splits in $K$ . Let $E_{1}$ and $E_{2}$ be elliptic curves over $K$ such that the $G a l (K ˉ / K)$ -modules $E_{1} [p]$ …

math.NT2024

Arithmetic statistics for Galois deformation rings

Anwesh Ray, Tom Weston

Given an elliptic curve $E$ defined over the rational numbers and a prime $p$ at which $E$ has good reduction, we consider the Galois deformation ring parametrizing lifts of the re…