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Article Dans Une Revue Journal de l'École polytechnique — Mathématiques Année : 2021

Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions

Résumé

We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular cases of interest, such as shift difference equations, q-dilation difference equations, Mahler difference equations, and elliptic difference equations. These criteria are obtained as an application of differential Galois theory for difference equations. We apply our criteria to prove a new result to the effect that most elliptic hypergeometric functions are differentially transcendental.
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Dates et versions

hal-03361384 , version 1 (01-10-2021)

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Carlos E Arreche, Thomas Dreyfus, Julien Roques. Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions. Journal de l'École polytechnique — Mathématiques, 2021, 8, pp.147-168. ⟨10.5802/jep.143⟩. ⟨hal-03361384⟩
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