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Miklos Schweitzer 1975_4

Source: multiplicative arithmetical functions form isomorphic groups

December 30, 2008
functionreal analysisnumber theory proposednumber theory

Problem Statement

Prove that the set of rational-valued, multiplicative arithmetical functions and the set of complex rational-valued, multiplicative arithmetical functions form isomorphic groups with the convolution operation f∘g f \circ g defined by (f∘g)(n)=∑d∣nf(d)g(nd).{ (f \circ g)(n)= %Error. "displatmath" is a bad command. \sum_{d|n} f(d)g(\frac nd}). (We call a complex number <spanclass=′latex−italic′>complexrational</span> <span class='latex-italic'>complex rational</span>, if its real and imaginary parts are both rational.) B. Csakany
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