Geodesic
Linear independence of values of Lerch functions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 56-59

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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. 
@article{VMUMM_2009_2_a10,
     author = {E. A. Ulanskii},
     title = {Linear independence of values of {Lerch} functions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {56--59},
     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_2_a10/}
}
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E. A. Ulanskii. Linear independence of values of Lerch functions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 56-59. http://geodesic.mathdoc.fr/item/VMUMM_2009_2_a10/