(Non)Automaticity of number theoretic functions
| dc.creator | Coons, Michael | |
| dc.date | 2008-10-21 | |
| dc.date | 2008-10-29 | |
| dc.date.accessioned | 2026-07-07T10:13:48Z | |
| dc.date.available | 2026-07-07T10:13:48Z | |
| dc.description | Denote by $λ(n)$ Liouville's function concerning the parity of the number of prime divisors of $n$. Using a theorem of Allouche, Mendès France, and Peyrière and many classical results from the theory of the distribution of prime numbers, we prove that $λ(n)$ is not $k$--automatic for any $k> 2$. This yields that $\sum_{n=1}^\infty λ(n) X^n\in\mathbb{F}_p[[X]]$ is transcendental over $\mathbb{F}_p(X)$ for any prime $p>2$. Similar results are proven (or reproven) for many common number--theoretic functions, including $ϕ$, $μ$, $Ω$, $ω$, $ρ$, and others. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0810.3709 | |
| dc.identifier | http://arxiv.org/abs/0810.3709 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172659 | |
| dc.subject | Number Theory | |
| dc.subject | 11J91; 11B85; 11N64 | |
| dc.title | (Non)Automaticity of number theoretic functions | |
| dc.type | text |