Nikisin  proved the linear independence of special values of polylogarithm functions over the rational number field. (see Theorem 0.1). In this paper, we give a generalization of the above result of Nikisin to the case of the Lerch function.
"Evaluation of the dimension of the Q-vector space spanned by the special values of the Lerch function." Tsukuba J. Math. 38 (2) 171 - 188, March 2015. https://doi.org/10.21099/tkbjm/1429103719