Number Theory Seminar
Tung T. Nguyen
Western University
Fekete polynomials, quadratic residues, and arithmetics
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
Friday February 11, 2022 at 1:00 PM in Zoom