p-adic interpolation and continuation of p-adic functions. (English) Zbl 0542.12009

Hà Huy Khoái

Complex analysis - Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math. 1013, 252-265 (1983).

[For the entire collection see Zbl 0516.00016.]
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.

Reviewer: M.van der Put

MSC:

11S80	Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
30G06	Non-Archimedean function theory
12J25	Non-Archimedean valued fields

Keywords:

continuation of p-adic functions; Mellin-Mazur transform; p-adic interpolation; L-functions; Gauss-sums

Citations:

Zbl 0516.00016