activity
20242026
collaborators

6 papers

math.NT2026

Counting number fields of fixed degree by their smallest defining polynomial

Santiago Arango-Piñeros, Fabian Gundlach, Robert J. Lemke Oliver +5

When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of on the space of polynom…

math.NT2025

The least prime with a given cycle type

Peter J. Cho, Robert J. Lemke Oliver, Asif Zaman

Let be a finite group. Let be a Galois extension of number fields with Galois group isomorphic to , and let be a conjugacy inv…

math.NT2025

Asymptotics for -torsion and -extensions

Peter Koymans, Robert J. Lemke Oliver, Efthymios Sofos +1

We prove a composite case of the Cohen--Lenstra--Gerth heuristics. Specifically, we establish an asymptotic for the average -torsion of the class group of quadratic number field…

math.NT2025

Improving the trivial bound for -torsion in class groups

Robert J. Lemke Oliver, Asif Zaman

For any number field with and any integer , we improve over the commonly cited trivial bound $|\mathrm{Cl}_K[\ell]| \leq |\mathrm{Cl}_K| \…

math.NT2024

Enumerating Galois extensions of number fields

Robert J. Lemke Oliver

Let be a number field. We provide an asymptotic formula for the number of Galois extensions of with absolute discriminant bounded by some , as . We al…

math.NT2024

Faithful Artin induction and the Chebotarev density theorem

Robert J. Lemke Oliver, Alexander Smith

Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequ…