ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

2020/11/09 by CLEMENS FUCHS, SEBASTIAN HEINTZE · 3 citations
Computer Science · Mathematics · #Coding theory and cryptography #semigroups and automata theory #Meromorphic and Entire Functions

paper · pdf · doi:10.1017/s0004972720001094

Abstract

Abstract Let (G_n)_n=0^∞ be a nondegenerate linear recurrence sequence whose power sum representation is given by G_n = a₁(n) α ₁ⁿ + ⋯ + a_t(n) α _tⁿ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, |G_n| ≥ ( max _{j=1,… ,t} |α _j| )^{n(1-ε )} for n large enough.

Citations

• The zero multiplicity of linear recurrence sequences
• On composite lacunary polynomials and the proof of a conjecture of Schinzel

Cited by

• Quantitative growth of multi-recurrences
• S-units and period length of continued fractions of linear recursions
• On the growth of multi-recurrences. [europepmc]

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