대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권3호
  • /
  • Pages.717-734
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  • 2015
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS

  • Cho, Ilwoo (Department of Mathematics St. Ambrose University)
  • 투고 : 2013.02.21
  • 발행 : 2015.05.31
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초록

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 $({\bullet});(t_1,t_2){\bullet}(s_1,s_2)=(t_1s_1,t_1s_2+t_2s_1)$.

키워드

참고문헌

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피인용 문헌

  1. Correction: An Application of Free Probability to Arithmetic Functions 2016, https://doi.org/10.1007/s11785-016-0604-x
  2. Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function vol.3, pp.4, 2015, https://doi.org/10.3390/math3041095
  3. Free probability on $$W^{*}$$ W ∗ -dynamical systems determined by $$GL_{2}(\mathbb {Q} _{p})$$ G L 2 ( Q p ) : generalized Hecke algebras 2016, https://doi.org/10.1007/s40574-016-0111-z