an:07225804
Zbl 1453.11004
Haukkanen, Pentti; Merikoski, Jorma K.; Tossavainen, Timo
Arithmetic subderivatives: \(p\)-adic discontinuity and continuity
EN
J. Integer Seq. 23, No. 7, Article 20.7.3, 17 p. (2020).
00451292
2020
j
11A25 11S82 26A15
arithmetic subderivative; arithmetic partial derivative; arithmetic derivative; continuity; \(p\)-adic absolute value
Summary: In a previous paper, we proved that the arithmetic subderivative \(D_S\) is discontinuous at any rational point with respect to the ordinary absolute value. In the present paper, we study this question with respect to the \(p\)-adic absolute value. In particular, we show that \(D_S\) is in this sense continuous at the origin if \(S\) is finite or \(p \not\in S\).