Zur Transzendenz gewisser Reihen. (On the transcendence of certain series). (German) Zbl 0601.10025

W. M. Schmidt’s famous theorem on the simultaneous approximation of algebraic numbers is used to derive transcendence results concerning certain series of rational numbers. The denominators of these numbers are taken from finitely many linear recursive sequences with the same characteristic polynomial which in turn is the minimal polynomial of a PV number. These denominators have to satisfy a divisibility as well as a growth condition (and in an appendix of the paper the second author studies the connections between these two kinds of hypotheses). The nominators of the rational terms of the series must satisfy some growth conditions too.
One section of the present paper is devoted to the study of the implications of Mahler’s analytic transcendence method from 1929 to the arithmetical questions considered here.


11J81 Transcendence (general theory)
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11B37 Recurrences
Full Text: DOI EuDML


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