Tung T. Nguyen : Fekete polynomials, quadratic residues, and arithmetics

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

At

Feb. 11, 2022, 1 p.m.

In

Zoom

Abstract

Fekete polynomials play an important role in the study of special values of L-functions of quadratic fields. While their analytic properties are well-studied in the literature, little is known about their arithmetics. In this talk, we will discuss some surprising arithmetical properties of these polynomials. In particular, we will see that special values of Fekete polynomials contain some rich information about the class numbers of quadratic fields. Furthermore, their Galois groups seem to follow a rather simple pattern. Time permitting, I will discuss some recent progress on generalized Fekete polynomials. This is based on joint work with Jan Minac and Nguyen Duy Tan.

Zoom link: https://uic.zoom.us/j/88173268700?pwd=aEhmTGpSOVhidWE4L1VWUnNhNVlvUT09