2 papers
math.NT2025
An Explicit Tauberian Theorem taking Averaged Inputs with an Application to Counting Abelian Number Fields
Brandon Alberts
Given a Dirichlet series , the asymptotic growth rate of can be determined by a Tauberian theorem. Bounds on the error term are typicall…
math.NT2025
Inductive methods for counting number fields
Brandon Alberts, Robert J. Lemke Oliver, Jiuya Wang +1
We give a new method for counting extensions of a number field asymptotically by discriminant, which we employ to prove many new cases of Malle's Conjecture and counterexamples to…