10.46298/hrj.2015.1358
https://hrj.episciences.org/1358
Bundschuh, Peter
Peter
Bundschuh
Väänänen, Keijo
Keijo
Väänänen
Algebraic independence results on the generating Lambert series of the powers of a fixed integer
In this paper, the algebraic independence of values of the functionG d (z) := h≥0 z d h /(1 − z d h), d > 1 a fixed integer, at non-zero algebraic points in the unit disk is studied. Whereas the case of multiplicatively independent points has been resolved some time ago, a particularly interesting case of multiplicatively dependent points is considered here, and similar results are obtained for more general functions. The main tool is Mahler's method reducing the investigation of the algebraic independence of numbers (over Q) to the one of functions (over the rational function field) if these satisfy certain types of functional equations.
episciences.org
algebraic independence of functions
Mahler's method
Algebraic independence of numbers
2010 Mathematics Subject Classification 11J91, 11J81, 39B32
[MATH] Mathematics [math]
2016-01-14
2015-01-01
2015-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01253655v1
2804-7370
https://hrj.episciences.org/1358/pdf
VoR
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Hardy-Ramanujan Journal
Volume 38 - 2015
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