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- Title
ARITHMETICAL RESULTS ON CERTAIN q-SERIES, II.
- Authors
BUNDSCHUH, PETER; VÄÄNÄNEN, KEIJO
- Abstract
As in Part I, entire transcendental solutions of certain mth order linear q-difference equations are investigated arithmetically, where now the polynomial coefficients are much more general. The purpose of this paper is to produce again lower bounds for the dimension of the K-vector space generated by 1 and the values of these solutions at m successive powers of q, where K is the rational or an imaginary quadratic field. A new feature in the proof is to use simultaneously positive and negative powers of q as interpolation points leading to an extra parameter in the main result extending its applicability.
- Subjects
Q-series; FUNCTIONAL analysis; QUADRATIC fields; DIFFERENCE equations; VECTOR analysis
- Publication
International Journal of Number Theory, 2009, Vol 5, Issue 7, p1231
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042109002663