Fekete polynomials : Real zeros, Mahler measure, and applications

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Fekete polynomials are certain Littlewood type polynomials whose coefficients are the values of the Legendre symbol, or more generally the Kronecker symbol. These polynomials were considered by Fekete in an attempt to understand real zeros of Dirichlet L-functions in the critical strip. Since then, their zeros and value distribution have been extensively studied. In this talk I will present some recent results concerning real zeros and the Mahler measure of Fekete polynomials.  We shall also discuss applications to sign changes of quadratic character sums. This is a joint work with O. Klurman and M. Munsch.