International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3997-4017
doi:10.1155/IJMMS.2005.3997
Properties of rational arithmetic functions
Vichian Laohakosol1
and Nittiya Pabhapote2
1Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
2Department of Mathematics, School of Science, University of the Thai Chamber of Commerce, Bangkok 10400, Thailand
Abstract
Rational arithmetic functions are arithmetic functions of the form g1∗⋯∗gr∗h1−1∗⋯∗hs−1, where gi, hj are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established; second, possible Busche-Ramanujan-type identities are investigated; third, binomial-type identities are derived; and finally, properties of the Kesava Menon norm of such functions are proved.