  In our work we have reconsidered the old problem of diffusion at the boundary
of ultrametric tree from a "number theoretic" point of view. Namely, we use the
modular functions (in particular, the Dedekind eta-function) to construct the
"continuous" analog of the Cayley tree isometrically embedded in the Poincare
upper half-plane. Later we work with this continuous Cayley tree as with a
standard function of a complex variable. In the frameworks of our approach the
results of Ogielsky and Stein on dynamics on ultrametric spaces are reproduced
semi-analytically/semi-numerically. The speculation on the new "geometrical"
interpretation of replica n->0 limit is proposed.
