JournalspmVol. 66, No. 4pp. 413–426

Series of reciprocal products with factors from linear recurrence sequences

  • Peter Bundschuh

    Universität zu Köln, Germany
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Abstract

.ions { line-height: 1.8; } .ions sub { margin-left: -.5ex; } .ions sup { vertical-align: 1.2ex; } In this article we study the values of power series ∑ zn/∏ji = 0 W(n + im)k at certain points of their domain of meromorphy from the arithmetical point of view. (Wn) is a sequence of non-zero integers satisfying a recurrence Wn + 1 = pWn + qWn − 1 with non-zero integers p, q such that the discriminant Δ = p2 + 4q is positive but not a square. The main interest is to characterize the situations, where these values lie in the real quadratic number field ℚ(√Δ) or even in ℚ, but we also include some transcendence problems.

Cite this article

Peter Bundschuh, Series of reciprocal products with factors from linear recurrence sequences. Port. Math. 66 (2009), no. 4, pp. 413–426

DOI 10.4171/PM/1851