Some characterizations of specially multiplicative functions
A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characteriz...
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| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203301139 |
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| _version_ | 1832552760537513984 |
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| author | Pentti Haukkanen |
| author_facet | Pentti Haukkanen |
| author_sort | Pentti Haukkanen |
| collection | DOAJ |
| description | A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function
fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide
some further characterizations of specially multiplicative functions. |
| format | Article |
| id | doaj-art-2d33a34a71b24daaa0dcfaf87801ddad |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2d33a34a71b24daaa0dcfaf87801ddad2025-02-03T05:57:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003372335234410.1155/S0161171203301139Some characterizations of specially multiplicative functionsPentti Haukkanen0Department of Mathematics, Statistics and Philosophy, University of Tampere, FIN-33014, FinlandA multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.http://dx.doi.org/10.1155/S0161171203301139 |
| spellingShingle | Pentti Haukkanen Some characterizations of specially multiplicative functions International Journal of Mathematics and Mathematical Sciences |
| title | Some characterizations of specially multiplicative functions |
| title_full | Some characterizations of specially multiplicative functions |
| title_fullStr | Some characterizations of specially multiplicative functions |
| title_full_unstemmed | Some characterizations of specially multiplicative functions |
| title_short | Some characterizations of specially multiplicative functions |
| title_sort | some characterizations of specially multiplicative functions |
| url | http://dx.doi.org/10.1155/S0161171203301139 |
| work_keys_str_mv | AT penttihaukkanen somecharacterizationsofspeciallymultiplicativefunctions |