On the range of Carmichael's universal-exponent function

Florian Luca, and Carl Pomerance. "On the range of Carmichael's universal-exponent function." Acta Arithmetica 162.3 (2014): 289-308. <http://eudml.org/doc/278960>.

@article{FlorianLuca2014,
abstract = {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.},
author = {Florian Luca, Carl Pomerance},
journal = {Acta Arithmetica},
keywords = {Carmichael function; Euler function; sieve},
language = {eng},
number = {3},
pages = {289-308},
title = {On the range of Carmichael's universal-exponent function},
url = {http://eudml.org/doc/278960},
volume = {162},
year = {2014},
}

TY - JOUR
AU - Florian Luca
AU - Carl Pomerance
TI - On the range of Carmichael's universal-exponent function
JO - Acta Arithmetica
PY - 2014
VL - 162
IS - 3
SP - 289
EP - 308
AB - 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.
LA - eng
KW - Carmichael function; Euler function; sieve
UR - http://eudml.org/doc/278960
ER -