  The Mahler measure of a polynomial $P$ in $n$ variables is defined as the
mean of $\log|P|$ 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 $\mathbb{Q}$). 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.
