Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T22:32:05.693Z Has data issue: false hasContentIssue false
  • English
  • Français

on the value set of the Carmichael λ-function

Part of: Multiplicative number theory

Published online by Cambridge University Press:  09 April 2009

John B. Friedlander  and
Florian Luca
John B. Friedlander
Affiliation:
Department of MathematicsUniversity of TorontoToronto, Ontario M5S 3G3Canada e-mail: frdlndr@math.toronto.edu
Florian Luca
Affiliation:
Instituto de Matemáticas Universidad Nacional Autónoma de MéxicoC.P. 58180, Morelia, MichoacánMéxico e-mail: fluca@matmor.unam.mx
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.

In this paper we study the size of the value set of the Carmichael λ-functions.

MSC classification

Secondary: 11N25: Distribution of integers with specified multiplicative constraints 11N56: Rate of growth of arithmetic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 1 , February 2007 , pp. 123 - 131
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Banks, W. D., Friedlander, J. B., Luca, F., Pappalardi, F. and Shparlinski, I. E., ‘Coincidences in the values of the Euler and Carmichael functions’, Acta Arith. 122 (2006), 207–234.CrossRefGoogle Scholar
[2]Erdós, P., Pomerance, C. and Schmutz, E., ‘Carmichael's lambda function’, Acta Arith. 58 (1991), 363–385.CrossRefGoogle Scholar
[3]Erdós, P.Wagstaff, S. S. Jr, ‘The fractional parts of the Bernoulli numbers’, Illinois J. Math. 24 (1980), 104–112.CrossRefGoogle Scholar
[4]Ford, K., ‘The distribution of totients’, Ramanujan J. 2 (1998), 67–151.CrossRefGoogle Scholar
[5]Halberstam, H. and Richert, H.-E., Sieve methods (Academic Press, London, UK, 1974).Google Scholar
[6]Maier, H. and Pomerance, C., ‘On the number of distinct values of Euler's φ function’, Acta Arith. 49 (1988), 263–275.CrossRefGoogle Scholar
[7]Norton, K. K., ‘On the number of restricted prime factors of an integer. I’, Illinois J. Math. 20 (1976), 681–705.CrossRefGoogle Scholar
[8]Tenenbaum, G., Introduction to analytic and probabilistic number theory (University Press, Cambridge, UK, 1985).Google Scholar