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 , où est une suite récurrente de polynômes et un polynôme fixé. Ce problème a été étudié auparavant dans [14,15,16,17,32].
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 , where is a linear recurring sequence of polynomials and is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].
@article{JTNB_2005__17_3_749_0, author = {Clemens Fuchs and Attila Peth\H{o}}, title = {Effective bounds for the zeros of linear recurrences in function fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {749--766}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {3}, year = {2005}, doi = {10.5802/jtnb.518}, mrnumber = {2212123}, zbl = {05016585}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.518/} }
TY - JOUR AU - Clemens Fuchs AU - Attila Pethő TI - Effective bounds for the zeros of linear recurrences in function fields JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 749 EP - 766 VL - 17 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.518/ DO - 10.5802/jtnb.518 LA - en ID - JTNB_2005__17_3_749_0 ER -
%0 Journal Article %A Clemens Fuchs %A Attila Pethő %T Effective bounds for the zeros of linear recurrences in function fields %J Journal de théorie des nombres de Bordeaux %D 2005 %P 749-766 %V 17 %N 3 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.518/ %R 10.5802/jtnb.518 %G en %F JTNB_2005__17_3_749_0
Clemens Fuchs; Attila Pethő. Effective bounds for the zeros of linear recurrences in function fields. Journal de théorie des nombres de Bordeaux, Tome 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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