Linear independence of values of Tschakaloff functions with different parameters

We prove Q-linear independence results for the values of the q-seriesTqt(z)=∑ν=0∞q−tν(ν+1)/2zνandΘ(q−t,z)=∑ν=−∞∞q−tν2zν at different rational points z≠0 and with different positive integer parameters t, where q∈Z∖{0,±1}.