Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T11:56:04.963Z Has data issue: false hasContentIssue false
  • English
  • Français

On Arithmetic Convolutions

Published online by Cambridge University Press:  20 November 2018

T.M. K. Davison
T.M. K. Davison*
Affiliation:
University of Waterloo
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let A be the set of all functions from N, the natural numbers, to C the field of complex numbers. The Dirichlet product of elements f, g of A is given by

where the summation condition means sum over all positive integers d which divide n.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 3 , August 1966 , pp. 287 - 296
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Cashwell, E.D. and Everett, C.J., The ring of number theoretic functions. Pacific J. Math., 9(1959)975-985.Google Scholar
2. Cohen, E., Arithmetical functions associated with the unitary divisors of an integer, Math. Zeit., 74 (1960), 66-80.Google Scholar
3. Gioia, A. A., The K-product of arithmetic functions. Canadian Journal of Math., XVII (1965) 970-976.Google Scholar
4. Hardy, G.H. and Wright, E.M., An introduction to the theory of numbers, (Oxford, 3rd edition, 1954).Google Scholar
5. Le Veque, W. J., Topics in number theory I. (Reading, Addison-Wesley, 1956).Google Scholar
6. Narkiewicz, W., On a class of arithmetical convolutions, Colloq. Math., 10 (1963), 81-94.Google Scholar
7. Rankin, R. A., On the representation of a number as the sum of any number of squares, and in particular of twenty, Acta. Arith., 7(1962) 399-407.Google Scholar
8. Subba Rao, M.V. and Gioia, A. A., Generalized Dirichlet products of arithmetic functions (abstract), Amer. Math. Soc. Notices 10 (1963) No. 7, p. 661.Google Scholar
9. Vaidyanathaswamy, R., The theory of multiplicative arithmetical functions, Trans. Amer. Math. Soc, 33 (1931) 579-662.Google Scholar
10. Wintner, A., Eratosthenian averages, (Privately printed, Baltimore, 1943).Google Scholar