Automatic Dirichlet series

Authors
Allouche, JP France, MM Peyriere, J
Citation
Jp. Allouche et al., Automatic Dirichlet series, J NUMBER TH, 81(2), 2000, pp. 359-373
Citations number
15
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF NUMBER THEORY
ISSN journal
0022314X → ACNP
Volume
81
Issue
2
Year of publication
2000
Pages
359 - 373
Database
ISI
SICI code
0022-314X(200004)81:2<359:ADS>2.0.ZU;2-8
Abstract
Dirichlet series whose coefficients are generated by finite automats define meromorphic functions on the whole complex plane. As consequences, a new p roof of Cobham's theorem on the existence of logarithmic frequencies of sym bols in automatic sequences is given, and certain infinite products are exp licitly computed. (C) 2000 Academic Press.