3 papers
math.NT2025
A heuristic for ray class groups of quadratic number fields
Alex Bartel, Carlo Pagano
We formulate a model for the average behaviour of ray class groups of real quadratic fields with respect to a fixed rational modulus, locally at a finite set of odd primes. To…
math.NT2025
Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups
Alex Bartel, Adam Morgan
We address several seemingly disparate problems in arithmetic geometry: the statistical behaviour of the Galois module structure of Mordell--Weil groups of a fixed elliptic curve o…
math.NT2018
On class groups of random number fields
Alex Bartel, Hendrik W. Lenstra
The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in t…