Onp-adic functions preserving Haar measure

Let {a_n}_n^=0/ be a uniformly distributed sequence ofp-adic integers. In the present paper we study continuous functions close to differentiable ones (with respect to thep-adic metric); for these functions, either the sequence {f(a_n)}_n^=0/ is uniformly distributed over the ring ofp-adic integers or, for all sufficiently largek, the sequences {f_k(_k(a_n))}_n^=0/ are uniformly distributed over the residue class ring modp^k, where_k is the canonical epimorphism of the ring ofp-adic integers to the residue class ring modp^k andf_k is the function induced byf on the residue class ring modp^k (i.e.,f k_(x) =f(_k(x)) (modp^k)). For instance, these functions can be used to construct generators of pseudorandom numbers.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 935–950, June, 1998.In conclusion, the author wishes to express his deep gratitude to V. S. Anashin for permanent attention to this research and for support.