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.

number theory

Audience: researchers in the discipline

Comments: Register for the next session of NDNT Round 5 on February 15 using the following links:

uwmadison.zoom.us/meeting/register/tJMkc-2hqDojG9yua5n-EkWxonnHyGeeMJkJ

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POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

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