## 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 $$q\in \mathbb Z\backslash \{0,\pm 1\}$$.

### MSC:

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

### Keywords:

Chakalov functions; linear independence

Zbl 1173.11043
Full Text:

### References:

 [1] Amou, M.; Väänänen, K., On linear independence of theta values, Monatsh. math., 144, 1, 1-11, (2005) · Zbl 1066.11031 [2] Bundschuh, P., Arithmetical properties of functions satisfying linear q-difference equations: A survey, Analytic number theory—expectations for the 21st century, Proceedings of a symposium held at the RIMS, Kyoto University, Kyoto, October 23-27, 2000, Sūrikaisekikenkyūsho Kōkyūroku, 1219, 110-121, (2001) · Zbl 1047.11519 [3] Hardy, G.H.; Wright, E.M., An introduction to the theory of numbers, (1979), Oxford Univ. Press Oxford · Zbl 0423.10001 [4] Väänänen, K., On linear independence of the values of generalized heine series, Math. ann., 325, 1, 123-136, (2003) · Zbl 1025.11023 [5] Väänänen, K.; Zudilin, W., Linear independence of values of tschakaloff series, Uspekhi mat. nauk, Russian math. surveys, 62, 1, 196-198, (2007), (in Russian); English transl.: · Zbl 1173.11043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.