On the range of Carmichael's universal-exponent function

• Autorzy: Florian Luca , Carl Pomerance
• Języki publikacji: EN

Abstrakty

EN

Let λ denote Carmichael's function, so λ(n) is the universal exponent for the multiplicative group modulo n. It is closely related to Euler's φ-function, but we show here that the image of λ is much denser than the image of φ. In particular the number of λ-values to x exceeds $x/(log x)^{.36}$ for all large x, while for φ it is equal to $x/(log x)^{1+o(1)}$, an old result of Erdős. We also improve on an earlier result of the first author and Friedlander giving an upper bound for the distribution of λ-values.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 3
• Strony: 289-308

Daty

wydano

2014

Twórcy

autor

Florian Luca

• Mathematical Institute, UNAM Juriquilla, Juriquilla, 76230 Santiago de Querétaro, Querétaro de Arteaga, México
• School of Mathematics, University of the Witwatersrand, P.O. Box Wits 2050, Johannesburg, South Africa

autor

Carl Pomerance

• Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551, U.S.A.

Identyfikatory

DOI

10.4064/aa162-3-6