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

Alina Firicel (2013)

Acta Arithmetica

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...

Symmetry of iteration graphs

Walter Carlip, Martina Mincheva (2008)

Czechoslovak Mathematical Journal

We examine iteration graphs of the squaring function on the rings ℤ / n ℤ when n = 2 k p , for p a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when k = 3 and when k ≥ 5 and are symmetric when k = 4 .

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