eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2015-01-01
Volume 38 - 2015
10.46298/hrj.2015.1358
1358
journal article
Algebraic independence results on the generating Lambert series of the powers of a fixed integer
Peter Bundschuh
Keijo Väänänen
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.
https://hrj.episciences.org/1358/pdf
algebraic independence of functions
Mahler's method
Algebraic independence of numbers
2010 Mathematics Subject Classification 11J91, 11J81, 39B32
[MATH] Mathematics [math]