7 papers
The strong form of Van der Waerden's conjecture via twisted Chowla
Theresa C. Anderson, Sam Chow, Rainer Dietmann +3
Determining the properties of a random polynomial has fuelled significant investigation over the past century. One driving force of this research is a 1936 paper of Van der Waerden…
Effective Brauer-Siegel theorems for Artin -functions
Peter J. Cho, Robert J. Lemke Oliver, Asif Zaman
Given a number field , in a now classic work, Stark pinpointed the possible source of a so-called Landau-Siegel zero of the Dedekind zeta function and…
Counting number fields of fixed degree by their smallest defining polynomial
Santiago Arango-Piñeros, Fabian Gundlach, Robert J. Lemke Oliver +5
When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of on the space of polynom…
The least prime with a given cycle type
Peter J. Cho, Robert J. Lemke Oliver, Asif Zaman
Let be a finite group. Let be a Galois extension of number fields with Galois group isomorphic to , and let be a conjugacy inv…
Asymptotics for -torsion and -extensions
Peter Koymans, Robert J. Lemke Oliver, Efthymios Sofos +1
We prove a composite case of the Cohen--Lenstra--Gerth heuristics. Specifically, we establish an asymptotic for the average -torsion of the class group of quadratic number field…
Characterizing the support of semiclassical measures for higher-dimensional cat maps
Elena Kim, Theresa C. Anderson, Robert J. Lemke Oliver
Quantum cat maps are toy models in quantum chaos associated to hyperbolic symplectic matrices . The macroscopic limits of sequences of eigenf…