Algebra & Number Theory
- Algebra Number Theory
- Volume 11, Number 3 (2017), 685-712.
Automatic sequences and curves over finite fields
We prove that if a is an algebraic power series of degree , height , and genus , then the sequence a is generated by an automaton with at most states, up to a vanishingly small error term. This is a significant improvement on previously known bounds. Our approach follows an idea of David Speyer to connect automata theory with algebraic geometry by representing the transitions in an automaton as twisted Cartier operators on the differentials of a curve.
Algebra Number Theory, Volume 11, Number 3 (2017), 685-712.
Received: 20 June 2016
Revised: 20 November 2016
Accepted: 19 December 2016
First available in Project Euclid: 19 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11B85: Automata sequences
Secondary: 11G20: Curves over finite and local fields [See also 14H25] 14H05: Algebraic functions; function fields [See also 11R58] 14H25: Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
Bridy, Andrew. Automatic sequences and curves over finite fields. Algebra Number Theory 11 (2017), no. 3, 685--712. doi:10.2140/ant.2017.11.685. https://projecteuclid.org/euclid.ant/1508431777