Multiplicative functions and $k$-automatic sequences

Yazdani, Soroosh. "Multiplicative functions and $k$-automatic sequences." Journal de théorie des nombres de Bordeaux 13.2 (2001): 651-658. <http://eudml.org/doc/248691>.

@article{Yazdani2001,
abstract = {A sequence is called $k$-automatic if the $n$’th term in the sequence can be generated by a finite state machine, reading $n$ in base $k$ as input. We show that for many multiplicative functions, the sequence $(f (n) \text\{ mod \} v)_\{n \ge 1\}$ is not $k$-automatic. Among these multiplicative functions are $\gamma _m(n), \sigma _m(n), \mu (n)$ et $\phi ( n)$.},
author = {Yazdani, Soroosh},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {multiplicative functions; finite automata; transcendence},
language = {eng},
number = {2},
pages = {651-658},
publisher = {Université Bordeaux I},
title = {Multiplicative functions and $k$-automatic sequences},
url = {http://eudml.org/doc/248691},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Yazdani, Soroosh
TI - Multiplicative functions and $k$-automatic sequences
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 2
SP - 651
EP - 658
AB - A sequence is called $k$-automatic if the $n$’th term in the sequence can be generated by a finite state machine, reading $n$ in base $k$ as input. We show that for many multiplicative functions, the sequence $(f (n) \text{ mod } v)_{n \ge 1}$ is not $k$-automatic. Among these multiplicative functions are $\gamma _m(n), \sigma _m(n), \mu (n)$ et $\phi ( n)$.
LA - eng
KW - multiplicative functions; finite automata; transcendence
UR - http://eudml.org/doc/248691
ER -