9 citations · 21 across the 8 of their papers we have counts for
10 papers
Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of and number fields
Brandon Alberts
We prove upper bounds for certain number field counting functions using Serre's modularity conjecture (now a theorem of Khare--Wintenberger). These results are comparable to sharp…
Counting number fields using multiple Dirichlet series
Brandon Alberts, Alina Bucur
We provide a method for counting number fields of fixed Galois group ordered by arbitrary inertial invariants using analytic techniques from the study of multiple Dirichlet series.…
A Random Group with Local Data Realizing Heuristics for Number Field Counting
Brandon Alberts
We define a group with local data over a number field as a group together with homomorphisms from decomposition groups . Such groups res…
Counting Functions for Random Objects in a Category
Brandon Alberts
In arithmetic statistics and analytic number theory, the asymptotic growth rate of counting functions giving the number of objects with order below is studied as .…
Harmonic Analysis and Statistics of the First Galois Cohomology Group
Brandon Alberts, Evan O'Dorney
We utilize harmonic analytic tools to count the number of elements of the Galois cohomology group with discriminant-like invariant as $X\to\inft…
Statistics of the First Galois Cohomology Group: A Refinement of Malle's Conjecture
Brandon Alberts
Malle proposed a conjecture for counting the number of -extensions with discriminant bounded above by , denoted , where is a fixed transitive subgroup $G\…
The Weak Form of Malle's Conjecture and Solvable Groups
Brandon Alberts
For a fixed finite solvable group and number field , we prove an upper bound for the number of -extensions with restricted local behavior (at infinitely many places…
Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations
Brandon Alberts
We study solutions to the Brauer embedding problem with restricted ramification. Suppose and are a abelian groups, is a central extension of by , and $f:\text{Ga…
The distribution of -extensions of quadratic fields
Brandon Alberts, Jack Klys
We compute all the moments of a normalization of the function which counts unramified -extensions of quadratic fields, where is the quaternion group of order 8, and…
Cohen-Lenstra Moments for Some Nonabelian Groups
Brandon Alberts
Cohen and Lenstra detailed a heuristic for the distribution of odd p-class groups for imaginary quadratic fields. One such formulation of this distribution is that the expected num…