Unitary Convolution and Generalized MӦbius Function
Article Sidebar
Main Article Content
Abstract
The concept of unitary convolution in the commutative ring of arithmetic functions, under the two operations of addition and unitary convolution, is investigated. A generalized unitary MӦbius function is defined and its basic properties, which extend those corresponding classical ones are derived. Of particular interest are certain generalized unitary MӦbius inversion formula and some characterizations of multiplicative functions.
Keywords: arithmetic function, Mӧbius inversion formula, multiplicative function, unitary convolution
*Corresponding author: Tel.: +66 851421272
E-mail: [email protected]
Article Details
Copyright Transfer Statement
The copyright of this article is transferred to Current Applied Science and Technology journal with effect if and when the article is accepted for publication. The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, electronic form (offline, online) or any other reproductions of similar nature.
The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
Here is the link for download: Copyright transfer form.pdf
References
[2] Cohen, E., 1960. Arithmetical functions associated with the unitary divisors of aninteger. Math. Zeitschr., 74, 66-80.
[3] Cohen, E., 1961. Unitary products of arithmetical functions. Acta Arith., 7, 29-38.
[4] Cohen, E., 1964. Arithmetical notes. X. A class of to tients. Proc. Amer. Math. Soc., 15(4), 534-539.
[5] Horadam, E.M., 1962. Arithmetical function associated with the unitary divisors of a generalized integer. Amer. Math. Monthly, 69, 196-199.
[6] Rao, K.N., 1965. On the unitary an alogues of certain totients. Monatsh. Math., 70, 149-154.
[7] Vaidyanathaswamy, R., 1931. The theory of multiplicative arithmetic functions. Trans. Amer. Math. Soc., 33, 579-662.
[8] Rearick, D., 1968. Operators on algebras of arithmetic functions. Duke. Math. J., 35, 761-766.
[9] Hansen, R.T. and Swanson L.G., 1979. Unitary divisors. Math. Magazine, 52, 217-222.
[10] Johnson, K.R., 1982. Unitary an alog of generalized Ramanujan sums. Pacific J. Math., 103, 429-432.
[11] Hsu, L.C., 1995. A difference-operational approach to the Mӧbius inversion formulas. Fibonacci Quarterly, 33, 169-173.
[12] Hsu, L.C. and Wang J., 1998. Some Mӧbius-type functions and inversions constructed via difference operators. Tamkang J. Math., 29, 89-99.
[13] Schinzel, A., 1998. A property of unitary convolution. Colloq. Math., 78, 93-96.
[14] Buschman, R.G., 2003. Unitary product again, StudiaUniv. Babes-Bolyai, Mathematica, 48, 29-34.