The image of Carmichael’s λ-function

Ford, Kevin; Luca, Florian; Pomerance, Carl

doi:10.2140/ant.2014.8.2009

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The image of Carmichael's $\lambda$-function

Kevin Ford, Florian Luca and Carl Pomerance

Vol. 8 (2014), No. 8, 2009–2026

DOI: 10.2140/ant.2014.8.2009

Abstract

We show that the counting function of the set of values of Carmichael’s $λ$ -function is $x ∕ {(log x)}^{η + o (1)}$ , where $η = 1 - (1 + log log 2) ∕ (log 2) = 0.08607 \dots$ .

Keywords

Carmichael's function, Carmichael's lambda function

Mathematical Subject Classification 2010

Primary: 11N64

Secondary: 11A25, 11N25

Milestones

Received: 23 June 2014

Revised: 4 September 2014

Accepted: 9 October 2014

Published: 28 November 2014

Authors

Kevin Ford
Department of Mathematics University of Illinois at Urbana–Champaign 1409 West Green Street Urbana, IL 61801 United States

Florian Luca
School of Mathematics University of the Witwatersrand P.O. Box Wits 2050 Johannesburg South Africa Instituto de Matématicas UNAM Juriquilla Santiago de Querétaro, 76230 Querétaro de Arteaga México

Carl Pomerance
Mathematics Department Dartmouth College Kemeny Hall Hanover, NH 03755 United States

Vol. 8, No. 8, 2014