Abstract
As a continuation of the previous work by the authors having the same title, we study the arithmetical nature of the values of certain q-hypergeometric series ø,(z; q) with a rational or an imaginary quadratic integer q with |q| > 1, which is related to a q-analogue of the Bessel function J 0(z). The main result determines the pairs (q, α) with α ∈ K for which ø(α; q) belongs to K, where K is an imaginary quadratic number field including q.
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References
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Amou, M., Katsurada, M., Väänänen, K. (2002). On the Values of Certain q-Hypergeometric Series II. In: Jia, C., Matsumoto, K. (eds) Analytic Number Theory. Developments in Mathematics, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3621-2_2
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DOI: https://doi.org/10.1007/978-1-4757-3621-2_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5214-1
Online ISBN: 978-1-4757-3621-2
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