Arithmetic differential operators on Z_p
Number Theory
2008-08-06 v1
Abstract
We prove that a function f from Z_p to itself is analytic if and only if it can be represented as f(x)=F(x, dx, ..., d^r x) where dx=(x-x^p)/p is the Fermat quotient operator and F is a restricted power series with coefficients in Z_p.
Cite
@article{arxiv.0808.0688,
title = {Arithmetic differential operators on Z_p},
author = {A. Buium and C. C. Ralph and S. R. Simanca},
journal= {arXiv preprint arXiv:0808.0688},
year = {2008}
}