  We introduce the notion of stringy E-function for an arbitrary normal
irreducible algebraic variety X with at worst log-terminal singularities. We
prove some basic properties of stringy E-functions and compute them explicitly
for arbitrary Q-Gorenstein toric varieties. Using stringy E-functions, we
propose a general method to define stringy Hodge numbers for projective
algebraic varieties with at worst Gorenstein canonical singularities. This
allows us to formulate the topological mirror duality test for arbitrary
Calabi-Yau varieties with canonical singularities. In Appendix we explain
non-Archimedian integrals over spaces of arcs. We need these integrals for the
proof of the main technical statement used in the definition of stringy Hodge
numbers.
