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A digit function with Thomae-like properties
Published online by Cambridge University Press: 23 January 2015
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Following a recent revival of interest in both Thomae's function and digit functions (see [1] and [2] respectively) we present here a function providing an appealing link between the two. The former, nowadays often cited in courses on real analysis, was given by Thomae in 1875; see also [3], [4] and [5]. This function, which we denote by g(x), has the following definition:
where it is so be assumed that gcd (p, q) = 1 when x is rational.
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