Arithmetic Subderivatives: p-adic Discontinuity and Continuity
Pentti Haukkanen and Jorma K. Merikoski
Faculty of Information Technology and Communication Sciences
FI-33014 Tampere University
Finland
Timo Tossavainen
Department of Arts, Communication and Education
Lulea University of Technology
SE-97187 Lulea
Sweden
Abstract:
In a previous paper, we proved that the arithmetic subderivative
DS 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 DS
is in this sense continuous at the origin
if S is finite or p ∉ S.
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(Concerned with sequences
A000040
A003415.)
Received April 3 2020; revised version received June 24 2020.
Published in Journal of Integer Sequences,
June 26 2020.
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