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

Title & Authors
CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS
Cho, Ilwoo;

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 $\small{A_p}$ of equivalence classes under the quotient on A by the identically-free-distributedness is isomorphic to an algebra $\small{\mathbb{C}^2}$, having its multiplication \$({\bullet});(t_1,t_2){\bullet}(s_1,s_2)
Keywords
arithmetic functions;arithmetic algebra;linear functionals;arithmetic probability spaces;free-moment L-functions;
Language
English
Cited by
1.
Correction: An Application of Free Probability to Arithmetic Functions, Complex Analysis and Operator Theory, 2016
2.
Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function, Mathematics, 2015, 3, 4, 1095
3.
Free probability on \$\$W^{*}\$\$ W ∗ -dynamical systems determined by \$\$GL_{2}(\mathbb {Q} _{p})\$\$ G L 2 ( Q p ) : generalized Hecke algebras, Bollettino dell'Unione Matematica Italiana, 2016
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