Non-vanishing at the central point of the Dedekind zeta functions of non-Galois cubic fields

Abstract: It is believed that for every $S_n$-number field, i.e. every degree extension of the rationals whose normal closure has Galois group $S_n$, the Dedekind zeta function is non-vanishing at the central point. In the case $n=2$ Soundararajan established, in spectacular work improving on earlier work of Jutila, the non-vanishing of the Dedekind zeta function for at least 87.5% of the fields in certain families of quadratic fields. In this talk, I will present joint work with Arul Shankar and Nicolas Templier, in which we study the case $n=3$. In particular, I will discuss some of the main ideas in our proof that the Dedekind zeta functions of infinitely many $S_3$-fields have non-vanishing central value.

number theory

Audience: researchers in the topic

Around Frobenius Distributions and Related Topics IV

Series comments: Registration is free, but all participants are required to register on the conference website.