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

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 \(q\in \mathbb Z\backslash \{0,\pm 1\}\).


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


Zbl 1173.11043
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