  Let $X$ be a smooth, compact, projective K\"ahler variety and $D$ be a
divisor of a holomorphic form $F$, and assume that $D$ is smooth up to
codimension two. Let $\omega$ be a K\"ahler form on $X$ and $K_{X}$ the
corresponding heat kernel which is associated to the Laplacian that acts on the
space of smooth functions on $X$. Using various integral transforms of $K_{X}$,
we will construct a meromorphic function in a complex variable $s$ whose
special value at $s=0$ is the log-norm of $F$ with respect to $\mu$. In the
case when $X$ is the quotient of a symmetric space, then the function we
construct is a generalization of the so-called elliptic Eisenstein series which
has been defined and studied for finite volume Riemann surfaces.
