FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 5, PAGES 31-39

**Remarks on linear independence of $q$-harmonic
series**

P. Bundschuh

Abstract

View as HTML
View as gif image

For any rational integer $q$, $|q|\; >\; 1$, the linear
independence over $$**Q** of the numbers
$1$, $$z_{q}(1), and $$z_{-q}(1) is proved;
here $$z_{q}(1) = å_{n=1}^{¥}1/(q^{n} - 1) is so-called
$q$-harmonic
series or $q$-zeta-value at the
point $1$.
Besides this, a measure of linear independence of these numbers
is established.

Location: http://mech.math.msu.su/~fpm/eng/k10/k105/k10503h.htm

Last modified: May 30, 2011