This is the 2/3/21 talk given by Jesse Thorner for the Vanderbilt number theory seminar.
Abstract: I will present some recent work with Robert Lemke Oliver
and Asif Zaman in which we noticeably expand the region in which
almost all Artin L-functions in certain families are holomorphic and
nonvanishing. This combines Galois theory, character theory, and
analytic number theory. These results are motivated by a wide range
of classically flavored applications; I will focus on applications to
the study of class groups of high-degree number fields.
![](https://s2.save4k.ru/pic/02EshNERmg8/maxresdefault.jpg)