Composite values of polynomial power sums
Annales Mathématiques Blaise Pascal, Tome 26 (2019) no. 1, pp. 1-24.

Let (G n (x)) n=0 be a d-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let m2 be a given integer. We ask for n such that the equation G n (x)=gh is satisfied for a polynomial g[x] with degg=m and some polynomial h[x] with degh>1. We prove that for all but finitely many n these decompositions can be described in “finite terms” coming from a generic decomposition parameterized by an algebraic variety. All data in this description will be shown to be effectively computable.

Publié le : 2020-01-21
DOI : https://doi.org/10.5802/ambp.380
Classification : 11B37,  12Y05,  11R58
Mots clés: Decomposable polynomials, linear recurrence sequences, Brownawell–Masser inequality
@article{AMBP_2019__26_1_1_0,
     author = {Clemens Fuchs and Christina Karolus},
     title = {Composite values of polynomial power sums},
     journal = {Annales Math\'ematiques Blaise Pascal},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {26},
     number = {1},
     year = {2019},
     pages = {1-24},
     doi = {10.5802/ambp.380},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2019__26_1_1_0/}
}
Fuchs, Clemens; Karolus, Christina. Composite values of polynomial power sums. Annales Mathématiques Blaise Pascal, Tome 26 (2019) no. 1, pp. 1-24. doi : 10.5802/ambp.380. https://ambp.centre-mersenne.org/item/AMBP_2019__26_1_1_0/

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