Rational approximations to algebraic Laurent series with coefficients in a finite field

• Autorzy: Alina Firicel
• Języki publikacji: EN

Abstrakty

EN

We give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give a few examples of algebraic Laurent series for which we are able to compute the exact value of the irrationality exponent.

Kategorie tematyczne

• 11J61: Approximation in non-Archimedean valuations
• 68R15: Combinatorics on words
• 11T99: None of the above, but in this section
• 11J82: Measures of irrationality and of transcendence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 157
• Numer: 4
• Strony: 297-322

Daty

wydano

2013

Twórcy

autor

Alina Firicel

• Institut Joseph Fourier, Université de Grenoble, 100 rue des maths, BP 74, 38402 St Martin d'Hères Cedex, France

Identyfikatory

DOI

10.4064/aa157-4-1