Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS

  • Cho, Ilwoo (Department of Mathematics St. Ambrose University)
  • Received : 2013.02.21
  • Published : 2015.05.31
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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 $({\bullet});(t_1,t_2){\bullet}(s_1,s_2)=(t_1s_1,t_1s_2+t_2s_1)$.

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