International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3997-4017
Properties of rational arithmetic functions
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.
Rational arithmetic functions are arithmetic functions of the form
, where , 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.