Linear independence of values of Lerch functions

The number of linearly independent numbers among $1,\Phi _1\left( z,\frac{p}{q}\right),\ldots,\Phi _a\left( z,\frac{p}{q}\right)$ is estimated depending on a natural number $a$, where $\Phi _s \left(z,\frac{p}{q}\right),\ s=1,2,\ldots$, are Lerch functions.