5 papers · 1 filter
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…
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…
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,…
Power Savings for Counting (Twisted) Abelian Extensions of Number Fields
Brandon Alberts
We prove significant power savings for the error term when counting abelian extensions of number fields (as well as the twisted version of these results for nontrivial Galois modul…
Restricting the Splitting Types of a Positive Density Set of Places in Number Field Extensions
Brandon Alberts
We prove necessary and sufficient conditions for a finite group with an ordering of -extensions to satisfy the following property: for every positive density set of places $…