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Diagonalization and rationalization of algebraic Laurent series

Boris Adamczewski, Jason P. Bell (2013)

Annales scientifiques de l'École Normale Supérieure

We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime p the reduction modulo p of the diagonal of a multivariate algebraic power series f with integer coefficients is an algebraic power series of degree at most p A and height at most A p A , where A is an effective constant that only depends on...

Dickson curves.

Gomez-Calderon, Javier (2006)

International Journal of Mathematics and Mathematical Sciences

Dickson Polynomials that are Permutations

Cipu, Mihai (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 11T06, 13P10.A theorem of S.D. Cohen gives a characterization for Dickson polynomials of the second kind that permutes the elements of a finite field of cardinality the square of the characteristic. Here, a different proof is presented for this result.Research supported by the CERES program of the Ministry of Education, Research and Youth, contract nr. 39/2002.

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