CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
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 p of equivalence classes under the quotient on A by the identically-free-distributedness is isomorphic to an algebra C2, having its multiplication (•); (t1, t2) • (s1, s2) = (t1s1, t1s2 + t2s1).
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 p of equivalence classes under the quotient on A by the identically-free-distributedness is isomorphic to an algebra C2, having its multiplication (•); (t1, t2) • (s1, s2) = (t1s1, t1s2 + t2s1).
참고문헌 (18)
- T. M. Apostol, "Modular Functions and Dirichilet Series in Number Theory" (1990), Springer-Verlag
- D. Bump, "Automorphic Forms and Representations", Cambridge Studies in Adv. Math, 55 (1996), Cambridge Univ. Press
- Ilwoo Cho, "Direct producted $W^{*}$-probability spaces and corresponding amalgamated free stochastic integration", 대한수학회보, 44(1), pp.131~150 (2007), 대한수학회
- Ilwoo Cho, "Group-freeness and certain amalgamated freeness", 대한수학회지, 45(3), pp.597~609 (2008), 대한수학회
- I. Cho, "On dynamical systems induced by the Adele ring", Global J. Sci. Frontier Research (2015)
- I. Cho, "Free distributional data of arithmetic functions and corresponding generating functions determined by gaps of primes", Compl. Anal. Opre. Theo, 8(2), pp.537~570 (2014)
- I. Cho, "Dynamical systems on arithmatic functions determined by primes", Banach J. Math. Anal, 9(9), pp.173~215 (2015)
- I. Cho, "Arithmetic functions and free moments of certain free random variables", ~ (2012)
- I. Cho, "C∗-subalgebras generated by partial isometries", J. Math. Phy (2009)
- I. Cho, "Free probability induced by electric resistance networks on energy Hilbert spaces", Opuscula Math, 31(4), pp.549~598 (2011)
- H. Davenport, "Multiplicative Number Theory" (2000), Springer-Verlag
- T. Gillespie, "Superposition of zeroes of automorphic L-functions and functoriality", Ph.D., pp.2011
- T. Gillespie, "Prime number theorems for Rankin-Selberg L-functions over number fields", Sci. China Math, 54(1), pp.35~46 (2011)
- "Introduction to Analytic Number Theory, Lecture Notes" (2006)[URL]
- F. Radulescu, "Random matrices, amalgamated free products and subfactors of the C∗-algebra of a free group of nonsingular index", Invent. Math, 115(2), pp.347~389 (1994)
- R. Speicher, "Combinatorial theory of the free product with amalgamation and operator-valued free probability theory", Mem. Amer. Math. Soc, 132(627), pp.x+88~ (1998)
- V. S. Vladimirov, "p-Adic Analysis and Mathematical Physics", Ser. Soviet & East European Math, 1 (1994), World Scientific
- D. Voiculescu, "Free Random Variables", CRM Monograph Series, 1 (1992)