Codecà, P. and Nair, M. (2008) Smooth numbers and the norms of arithmetic Dirichlet convolutions. Journal of Mathematical Analysis and Applications, 347(2), pp. 400-406. (doi: 10.1016/j.jmaa.2008.06.006)
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Publisher's URL: http://dx.doi.org/10.1016/j.jmaa.2008.06.006
Abstract
In this paper we consider the problem of exactly evaluating the p-norm of a linear operator linked with arithmetic Dirichlet convolutions. We prove that a simply derived upper bound for this norm is actually attained for several different classes of arithmetic functions including completely multiplicative functions, but not for certain multiplicative functions. Our proof depends fundamentally on the asymptotic distribution properties of smooth numbers.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Nair, Dr Mohan |
| Authors: | Codecà, P., and Nair, M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Mathematical Analysis and Applications |
| ISSN: | 0022-247X |
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