We consider multi-polylogarithm functions which are slightly different from the ordinary ones. These functions have two integral representations and an order structure similar to those of multiple zeta star values. We also give a necessary and sufficient condition for the set of values of our multi-polylogarithm functions to be a dense set.
The necessary and sufficient condition for an algebraic integer to be a Salem number
Reduction of points in the group of components
Subconvexity for $GL_{3}(R)$ $L$-Functions via Integral Representations
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