Composite values of polynomial power sums

Fuchs, Clemens; Karolus, Christina

doi:10.5802/ambp.380

Cited by 2 publications

(3 citation statements)

References 23 publications

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“…Throughout the paper we denote by K a function field in one variable over C. By L we usually denote a finite algebraic extension of K. For the convenience of the reader we give a short summary of the notion of valuations that can also be found in [4]. For c ∈ C and f (x) ∈ C(x), where C(x) is the rational function field over C, we denote by ν c ( f ) the unique integer such that…”

Section: Results and Notationsmentioning

confidence: 99%

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On the Growth of Linear Recurrences in Function Fields

Fuchs

Heintze

2020

Bull. Aust. Math. Soc.

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Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

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Section: Results and Notationsmentioning

confidence: 99%

“…In the proof given in the next section we will apply the following special case of Theorem 1 in [6]. 4 C. Fuchs and S. Heintze [4] LEMMA 2.3. Let K be as above and L be a finite extension of K of genus g. Furthermore, let α 1 , .…”

Section: Results and Notationsmentioning

confidence: 99%

On the Growth of Linear Recurrences in Function Fields

Fuchs

Heintze

2020

Bull. Aust. Math. Soc.

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“…topic has been studied in several papers [6][7][8] and relevant results will be mentioned later in the introduction. For A 0 (x), A 1 (x), G 0 (x), G 1 (x) ∈ C[x], let (G n (x)) ∞ n=0 be a minimal, non-degenerate and simple binary linearly recurrent sequence of polynomials defined by…”

Section: Kresomentioning

confidence: 99%

On decompositions of binary recurrent polynomials

Kreso

2022

Monatsh Math

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Polynomial decomposition expresses a polynomial f as the functional composition $$f=g\circ h$$ f = g ∘ h of lower degree polynomials g and h, and has various applications. In this paper, we will show that for a minimal, non-degenerate, simple, binary, linearly recurrent sequence $$(G_n(x))_{n=0}^\infty $$ ( G n ( x ) ) n = 0 ∞ of complex polynomials whose coefficients in the Binet form are constants, if $$G_n(x)=g(h(x))$$ G n ( x ) = g ( h ( x ) ) , then apart from some exceptional situations that have to be taken into account, the degree of g is bounded by a constant independent of n. We will build on a general but conditional result of this type that already exists in the literature. We will then present one Diophantine application of the main result.

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Composite values of polynomial power sums

Abstract: Cet article est mis à disposition selon les termes de la licence C C-4.0 F .

Cited by 2 publications

References 23 publications

On the Growth of Linear Recurrences in Function Fields

On the Growth of Linear Recurrences in Function Fields

On decompositions of binary recurrent polynomials

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