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http://dx.doi.org/10.4134/BKMS.2015.52.3.717

CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS  

Cho, Ilwoo (Department of Mathematics St. Ambrose University)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.3, 2015 , pp. 717-734 More about this Journal
Abstract
In this paper, we provide a classification of arithmetic functions in terms of identically-free-distributedness, determined by a fixed prime. We show then such classifications are free from the choice of primes. In particular, we obtain that the algebra $A_p$ of equivalence classes under the quotient on A by the identically-free-distributedness is isomorphic to an algebra $\mathbb{C}^2$, having its multiplication $({\bullet});(t_1,t_2){\bullet}(s_1,s_2)=(t_1s_1,t_1s_2+t_2s_1)$.
Keywords
arithmetic functions; arithmetic algebra; linear functionals; arithmetic probability spaces; free-moment L-functions;
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Times Cited By KSCI : 2  (Citation Analysis)
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