Properties of rational arithmetic functions
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,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3997 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |