Linear Independence of q-Analogues of Certain Classical Constants |
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Authors: | Peter Bundschuh Keijo Väänänen |
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Affiliation: | 1. Department of Mathematics, University of Cologne, Weyertal 86-90, 50931, K?ln, Germany 2. Department of Mathematical Sciences, University of Oulu, P.O.Box 3000, 90114, Oulu, Finland
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Abstract: | Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σn≥1 an/(qn ? 1) ? K for non-zero periodic sequences (an) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82 |
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