Silas Johnson : Counting Functions, Mass Formulas, and Heuristics for Number Fields

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

April 11, 2017, 11 a.m.

In

SEO 612

Abstract

The Malle-Bhargava heuristics give asymptotic predictions for the density of number fields of bounded discriminant with a given Galois group G, in terms of the number of G-extensions of p-adic fields $\mathbb Q_p$. These heuristics can also be applied when the discriminant is replaced by any of a wide variety of other “counting functions”. Motivated by field-counting heuristics, I'll introduce the idea of such alternate counting functions and how to build them, and discuss results on global mass formulas for alternate counting functions.