Remarks on linear independence of <Emphasis Type="Italic">q</Emphasis>-harmonic series |
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Authors: | P Bundschuh |
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Institution: | 1.Mathematisches Institut,Universit?t zu K?ln,K?ln,Germany |
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Abstract: | For any rational integer q, |q|?>?1, the linear independence over \( \mathbb{Q} \) of the numbers 1, ζ q (1), and ζ ?q (1) is proved; here \( {\zeta_q}(1) = \sum\limits_{n = 1}^\infty {\frac{1}{{{q^n} - 1}}} \) is the so-called q-harmonic series or the q-zeta-value at the point 1. Besides this, a measure of linear independence of these numbers is established. |
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