An analogue of Hilbert's tenth problem for p-adic entire functions

Publisher： Cambridge University Press

E-ISSN： 1943-5886|60|4|1301-1309

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.60, Iss.4, 1995-12, pp. : 1301-1309

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Abstract

Let p be a fixed prime integer, other than 2, Q p the field of p-adic numbers, and Ω p the completion of the algebraic closure of Q p . Let R p be the ring of entire functions in one variable t over Ω p ; that is, R p is the ring of functions f: Ω p → Q p such that f(t) is given by a power series around 0, of infinite radius of convergence:

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