Hostname: page-component-7c8c6479df-nwzlb Total loading time: 0 Render date: 2024-03-19T04:29:16.409Z Has data issue: false hasContentIssue false

A NOTE ON THE DISTRIBUTION FUNCTION OF $ \varphi (\lowercase {P}-1)/(\lowercase {P}-1)$

Published online by Cambridge University Press:  16 January 2013

JEAN-MARC DESHOUILLERS*
Affiliation:
Institut Mathématique de Bordeaux, UMR 5251, Université de Bordeaux et CNRS, 33405 TALENCE Cedex, France (email: jean-marc.deshouillers@math.u-bordeaux.fr)
MEHDI HASSANI
Affiliation:
Department of Mathematics, University of Zanjan, University Blvd., 45371-38791 Zanjan, Iran (email: mehdi.hassani@znu.ac.ir)
*
For correspondence; e-mail: jean-marc.deshouillers@math.u-bordeaux.fr
Rights & Permissions [Opens in a new window]

Abstract

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.

We study the differentiability of the limiting distribution function associated to the normalized Euler function defined on the shifted primes.

Type
Research Article
Copyright
Copyright © 2013 Australian Mathematical Publishing Association Inc.

Footnotes

To the memory of Alf van der Poorten, an inspiring mathematician and a friend

References

[1]Erdős, P., ‘Some remarks about additive and multiplicative functions’, Bull. Amer. Math. Soc. 52 (1946), 527537.CrossRefGoogle Scholar
[2]Erdős, P., ‘On the distribution of numbers of the form $\sigma (n)/n$ and on some related questions’, Pacific J. Math. 52 (1974), 5965.CrossRefGoogle Scholar
[3]Kátai, I., ‘On distribution of arithmetical functions on the set prime plus one’, Compositio Math. 19 (1968), 278289.Google Scholar
[4]Tenenbaum, G., Introduction à la théorie Analytique et Probabiliste des Nombres (Belin, Paris, 2008).Google Scholar
[5]Tjan, M. M., ‘On the question of the distribution of values of the Euler function $\varphi (n)$’, Litovsk. Mat. Sb. 6 (1966), 105119.Google Scholar
[6]Toulmonde, V., ‘Comportement au voisinage de 1 de la fonction de répartition de $\phi (n)/n$’, Int. J. Number Theory 5 (2009), 13471384.CrossRefGoogle Scholar