We introduce a generalized Mahler measure. It has relations to multiple sine functions and Dirichlet L-functions. In particular, we are able to express special values of Dirichlet L-functions by sum of logarithmic generalized Mahler measures.
We introduce multiple q-Mahler measures and we calculate some specific examples, where multiple q-analogues of zeta functions appear. We study also limits as the multiple q goes to 1.
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