Linear independence of values of Tschakaloff functions with different parameters

We prove ℚ-linear independence results for the values of the q-series T_q^t(z)= ∞ / ∑ / ν=0 q^{-tν(ν+1)/2_zν} and Θ(q^-t,z)= ∞ / ∑ / ν=-∞ q^-tν²_zν at different rational points z ≠ 0 and with different positive integer parameters t, where q ∈ ℤ {0, ± 1}.