Manfred Krüppel

Takagi\'s continuous nowhere differentiable function and binary digital sums

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 63, 37 - 54 (2008)

MSC: 11A63   Radix representation; digital problems {For metric results, see 11K16}
  39B22   Equations for real functions [See also 26A51, 26B25]
  26A30   Singular functions, Cantor functions, functions with other special properties
ZDM: -  
CR: -  
PACS: -  

Abstract:   In this paper we derive functional relations and explicit representations at dyadic points for Takagi's continuous nowhere differentiable function $T$ and also for functions which are connected with $T$. As consequence we get formulas for binary digital sums, namely the Trollope-Delange formula for the number of ones, a formula counting the zeros as well as a formula for the alternating sum of digits.

Keywords:   Takagi\'s continuous nowhere differentiable function, functional equations, Trollope-Delange formula for the sum-of-digits function, alternating sum of digits, Cantor sets.
Seite generiert am 18.11.2008,   17:06   Uhr