Effective bounds for the zeros of linear recurrences in function fields
Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 3, pp. 749-766.

In this paper, we use the generalisation of Mason’s inequality due to Brownawell and Masser (cf. [8]) to prove effective upper bounds for the zeros of a linear recurring sequence defined over a field of functions in one variable.

Moreover, we study similar problems in this context as the equation G n (x)=G m (P(x)),(m,n) 2 , where (G n (x)) is a linear recurring sequence of polynomials and P(x) is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].

Dans cet article, on utilise la généralisation de l’inégalité de Mason (due à Brownawell et Masser [8]) afin d’exhiber des bornes supérieures effectives pour les zéros d’une suite linéaire récurrente définie sur un corps de fonctions à une variable.

De plus, on étudie de problèmes similairs dans ce contexte, comme l’équation G n (x)=G m (P(x)),(m,n) 2 , où (G n (x)) est une suite récurrente de polynômes et P(x) un polynôme fixé. Ce problème a été étudié auparavant dans [14,15,16,17,32].

Published online:
DOI: 10.5802/jtnb.518
Clemens Fuchs 1; Attila Pethő 2

1 Institut für Mathematik Technische Universität Graz Steyrergasse 30 8010 Graz, Austria Current Address: Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, Postbus 9512, 2300 RA Leiden, The Netherlands
2 Institute of Informatics University of Debrecen, Debrecen Pf. 12 4010 Debrecen, Hungary
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Clemens Fuchs; Attila Pethő. Effective bounds for the zeros of linear recurrences in function fields. Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 3, pp. 749-766. doi : 10.5802/jtnb.518. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.518/

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