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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…
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…