Automatic Dirichlet Series

✍ Scribed by J.-P Allouche; M Mendès France; J Peyrière

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 142 KB
• Volume: 81
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1999.2487

✦ Synopsis

Dirichlet series whose coefficients are generated by finite automata define meromorphic functions on the whole complex plane. As consequences, a new proof of Cobham's theorem on the existence of logarithmic frequencies of symbols in automatic sequences is given, and certain infinite products are explicitly computed.