Effective bounds for the zeros of linear recurrences in function fields

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

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 3, page 749-766
  • ISSN: 1246-7405

Abstract

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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 ) ∈ 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].

How to cite

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Fuchs, Clemens, and Pethő, Attila. "Effective bounds for the zeros of linear recurrences in function fields." Journal de Théorie des Nombres de Bordeaux 17.3 (2005): 749-766. <http://eudml.org/doc/249449>.

@article{Fuchs2005,
abstract = {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 $G_n(x)=G_m(P(x)), (m,n)\in \{\mathbb\{N\}\}^2$, 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].},
affiliation = {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; Institute of Informatics University of Debrecen, Debrecen Pf. 12 4010 Debrecen, Hungary},
author = {Fuchs, Clemens, Pethő, Attila},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {3},
pages = {749-766},
publisher = {Université Bordeaux 1},
title = {Effective bounds for the zeros of linear recurrences in function fields},
url = {http://eudml.org/doc/249449},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Fuchs, Clemens
AU - Pethő, Attila
TI - Effective bounds for the zeros of linear recurrences in function fields
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 3
SP - 749
EP - 766
AB - 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 $G_n(x)=G_m(P(x)), (m,n)\in {\mathbb{N}}^2$, 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].
LA - eng
UR - http://eudml.org/doc/249449
ER -

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