Linear independence of values of Tschakaloff functions with different parameters. (English) Zbl 1173.11044

Väänänen, Keijo; Zudilin, Wadim

J. Number Theory 128, No. 9, 2549-2558 (2008).

See the review of the authors’ announcement in Zbl 1173.11043.
Summary: We prove \(\mathbb Q\)-linear independence results for the values of the \(q\)-series \[ T_{q^t} (z) = \sum _{\nu =0}^{\infty} q^{-t\nu (\nu+1)/2}z^{\nu}\text{ and } \varTheta (q^{-t}, z)= \sum _{\nu = -\infty}^{\infty}q^{-t\nu ^2}z^{\nu} \] at different rational points \(z\neq 0\) and with different positive integer parameters \(t\), where \(q\in \mathbb Z\backslash \{0,\pm 1\}\).

MSC:

11J72	Irrationality; linear independence over a field
11J82	Measures of irrationality and of transcendence

Keywords:

Chakalov functions; linear independence

Citations:

Zbl 1173.11043

References:

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