Linear independence measures for infinite products |
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| Authors: | Peter Bundschuh Keijo Väänänen |
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| Institution: | Mathematisches Institut der Universit?t zu K?ln, Weyertal 86–90,?50931 K?ln, Germany. e-mail: pb@math.uni-koeln.de, DE
Department of Mathematical Sciences, University of Oulu, PO Box 3000, 90401 Oulu, Finland. e-mail: kvaanane@sun3.oulu.fi, FI
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| Abstract: | Let f be an entire transcendental function with rational coefficients in its power series about the origin. Further, let f satisfy a functional equation f(qz)= (z−c)f(z)+Q(z) with and some particular c∈ℚ. Then the linear independence of 1,f(α), f(−α) over ℚ for non-zero α∈ℚ is proved, and a linear independence measure for these numbers is given. Clearly, for Q= 0 the function f can be written as an infinite product.
Received: 19 September 2000 / Revised version: 14 March 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 11J72 11J82 |
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