Abstract
This paper shows that any completely additive complex valued function over a principal configuration in the complex plane, having constant values in some discs, is the identically zero function. In other words, there exists no non-trivial completely additive complex valued function over a principal configuration in \(\mathbb{C}\) which assumes constant values in some domain.
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Dedicated to Professor Imre Kátai on the occasion of his 75th birthday
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Mehta, J. On arithmetical functions having constant values in some domain. Acta Math Hung 142, 110–117 (2014). https://doi.org/10.1007/s10474-013-0342-8
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DOI: https://doi.org/10.1007/s10474-013-0342-8