  We develop two applications of the Kronecker's limit formula associated to
elliptic Eisenstein series: A factorization theorem for holomorphic modular
forms, and a proof of Weil's reciprocity law. Several examples of the general
factorization results are computed, specifically for certain moonshine groups,
congruence subgroups, and, more generally, non-compact subgroups with one cusp.
In particular, we explicitly compute the Kronecker limit function associated to
certain elliptic points for a few small level moonshine groups.
