Arithmetic differential operators on \(\mathbb Z_p\). (English) Zbl 1209.30022
Considering the Fermat quotient operator \(\delta_{a}=\frac{a-a^{p}}{p}\) on the ring or \(p\)-adic integers, the authors prove that any arithmetic differential operator on \(\mathbb{Z}_{p}\) of order \(m\) is an analytic function of level \(m\), and conversely.
Reviewer: Mehmet Cenkci (Antalya)
MSC:
| 30G06 | Non-Archimedean function theory |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
References:
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