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MR2678974 (2011f:11123) 11N25 (11A15 11N37)
Borwein, Peter; Choi, Stephen K. K.; Coons, Michael Completely multiplicative functions taking values in $\{-1,1\}$. Trans. Amer. Math. Soc. 362 (2010), no. 12, 6279–6291.
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