ON THE TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF CERTAIN CONTINUED FRACTIONS

Authors
TOPFER T
Citation
T. Topfer, ON THE TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF CERTAIN CONTINUED FRACTIONS, Monatshefte fuer Mathematik, 117(3-4), 1994, pp. 255-262
Citations number
5
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Monatshefte fuer Mathematik → ACNP
ISSN journal
00269255
Volume
117
Issue
3-4
Year of publication
1994
Pages
255 - 262
Database
ISI
SICI code
0026-9255(1994)117:3-4<255:OTTAAI>2.0.ZU;2-2
Abstract
The transcendence of continued fractions alpha = [a0; a1, a2,...] is p roved under growth conditions involving the denominators q(n) of the c onvergents and shifted partial quotients a(n+k). Extending this idea, conditions for the algebraic independence of several continued fractio ns are given. The proofs use the approximation properties of continued fractions in combination with the Thue-Siegel-Roth Theorem or a crite rion for algebraic independence of Bundschuh.