On the Nevanlinna Order of Meromorphic Solutions to Linear Analytic Difference Equations |
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Authors: | Yik-Man Chiang Simon N M Ruijsenaars |
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Institution: | Hong Kong University of Science and Technology Centre for Mathematics and Computer Science, The Netherlands |
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Abstract: | For various classes of linear ordinary analytic difference equations with meromorphic coefficients, we study Nevanlinna order properties of suitable meromorphic solutions. For a large class of first-order equations with coefficient of order ρ∈0, ∞), we explicitly construct meromorphic solutions of order ≤ρ+ 1. For higher-order equations with coefficients of order ρ∈0, ∞), we show that meromorphic solutions with increase of order ≤ρ+ 1 in a certain strip have order ≤ρ+ 1. The assumptions made in the latter setting may seem quite restrictive, but they are satisfied for several classes of second-order difference equations that have been studied in recent years. The latter include Harper-type equations, "reflectionless" equations, Askey–Wilson-type equations, and equations of relativistic Calogero–Moser type. |
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