Mahler measures, K-theory and values of L-functions

الأصل · EN

The Mahler measure of a polynomial P in n variables is defined as the mean of |P| over the n-dimensional torus. For certain polynomials with integer coefficients in two variables the Mahler measure is known to be related to special values of L-functions of arithmetic objects (e.g. Dirichlet characters and elliptic curves over Q). Inspired by work of Deninger Boyd has investigated this relationship numerically. In this paper we reduce some conjectures of Boyd to Beilinson`s conjectures on special values of L-functions. The methods in use are widely of K-theoretical nature.