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Remarque Sur un Article de T. M. Apostol

Published online by Cambridge University Press:  20 November 2018

Jean-Marie de Koninck  and
Armel Mercier
Jean-Marie de Koninck
Affiliation:
Dépt. de Math. Université du Québec Chicoutimi, Quebec
Armel Mercier
Affiliation:
Dépt. de Math. Université du Québec Chicoutimi, Quebec
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Dans un récent article [1], T. M. Apostol obtient une identité liant et , où f est une fonction complètement multiplicative, |f(n)| ≤ l, et p est un nombre premier. Il utilise cette identité pour prouver que

pour tout nombre premier p. Par la suite, T. M. Apostol obtenait d'autres identités [2].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 77 - 88
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Apostol, T. M., Identities of the type Proceedings of the A.M.S., Vol. 40 (1973), 341-345.Google Scholar
2. Apostol, T. M., Note on series of the type Nordisk Matematisk Tidskrift, 23 (1975), 49-50.Google Scholar
3. Ayoub, R., An introduction to the analytic theory of numbers, Amer. Math. Soc., Mathematical Surveys, no. 10, 1963, (reprinted 1974).Google Scholar
4. Ayoub, R., Euler and the zeta formula, Amer. Math. Monthly, Vol. 81 (1974), 1067-1086.Google Scholar
5. De Koninck, J. M., On a class of arithmetical functions, Duke Math. J. Vol. 39 (1972), 807-818.Google Scholar
6. Selberg, Atle, Note on a paper by L. G. Sathe, J. Indian Math. Soc., Vol. 18(1954), 83-87.Google Scholar