Let $${\mathbb{C}}_ p$$ denote the completion of the algebraic closure of $${\mathbb{Q}}_ p$$ and T the open unit disc in $${\mathbb{C}}_ p$$. For a discrete sequence $$u=(u_ 0,u_ 1,...)$$ in T the author considers the interpolation problem for holomorphic and meromorphic functions on T. This theory is then used to give proofs of interpolation statements on L- functions, Gauss-sums etc., which have been proved by B. Mazur, K. Iwasawa, K. Mahler, Y. Amice.
 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.) 30G06 Non-Archimedean function theory 12J25 Non-Archimedean valued fields