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

Received 13 January 2005; Revised 20 September 2005

Copyright © 2005 Vichian Laohakosol and Nittiya Pabhapote. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.