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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…
math.NT2024
Explicit Analytic Continuation of Euler Products
Brandon Alberts
The generating series of a number of different objects studied in arithmetic statistics can be built out of Euler products. Euler products often have very nice analytic properties,…