On the non-quadraticity of values of the q-exponential function and related q-series

Title: On the non-quadraticity of values of the q-exponential function and related q-series
Creator: Krattehthaler, Christian; Rochev, Igor; Väänänen, Keijo; Zudilin, W.
Relation: Acta Arithmetica Vol. 136, p. 243-269
Publisher Link: http://dx.doi.org/10.4064/aa136-3-4
Publisher: Polska Akademia Nauk Instytut Matematyczny
Resource Type: journal article
Date: 2009
Description: We investigate arithmetic properties of values of the entire function F(z) = F_q(z;λ)=[formula could not be replicated], |q|>1, λ ∉ q^ℤ>0 that includes as special cases the Tschakaloff function (λ = 0) and the q-exponential function (λ = 1). In particular, we prove the non-quadraticity of the numbers F_{q/sub>(α;λ) for integral q, rational λ and α ∉ -λq^ℤ>0, α ≠ 0.}
Subject: irrationality; non-quadraticity; q-exponential function; Hankel determinant; cyclotomic polynomial
Identifier: http://hdl.handle.net/1959.13/934852
Identifier: uon:11917
Identifier: ISSN:0065-1036
Language: eng
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