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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...

Explicit form for the discrete logarithm over the field GF ( p , k )

Gerasimos C. Meletiou (1993)

Archivum Mathematicum

For a generator of the multiplicative group of the field G F ( p , k ) , the discrete logarithm of an element b of the field to the base a , b 0 is that integer z : 1 z p k - 1 , b = a z . The p -ary digits which represent z can be described with extremely simple polynomial forms.

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