Abstract
Let f be an additive number-theoretical function and q≥1. We give necessary and sufficient conditions for f to satisfy
. By means of this characterization we show that f is
if and only if the above condition is satisfied and f has a mean value; in this case the Ramanujan expansion of f converges pointwise to f.
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Hildebrand, A., Spilker, J. Charakterisierung der additiven, fast-geraden Funktionen. Manuscripta Math 32, 213–230 (1980). https://doi.org/10.1007/BF01299602
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DOI: https://doi.org/10.1007/BF01299602