The Mahler measure of exact polynomials and L-function of motives   

Abstract: The Mahler measure of polynomials was introduced by Mahler in 1962 as a tool to study transcendental number theory. Over time, numerous connections have been discovered between Mahler measure and special values of L-functions. In this talk, we express the Mahler measure of an exact polynomial in arbitrarily many variables in terms of Deligne–Beilinson cohomology, and study its relationship with Beilinson regulators. As an application, we show that the Mahler measure of certain three-variable polynomials can be expressed in terms of special values of the L-functions of elliptic curves and the Bloch–Wigner dilogarithm. In the four-variable case, the Mahler measure can be written as a linear combination of special values of the L-functions of K3 surfaces and of the Riemann zeta function.

Spiegelgasse 5, Seminarraum 05.002