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Zeta functions connecting multiple zeta values and poly-Bernoulli numbers
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We first review our previous works of Arakawa and the authors on two, closely related single-variable zeta functions. Their special values at positive and negative integer arguments are respectively multiple zeta values and poly-Bernoulli numbers. We then introduce, as a generalization of Sasaki's work, level 2 analogue of one of the two zeta functions and prove results analogous to those by Arakawa and the first named author.
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Evaluations of multiple polylogarithm functions, multiple zeta values and related zeta values
The author proves several 1997 Borwein-Bradley-Broadhurst conjectures and general reduction formulas for alternating multiple zeta values using iterated integrals.
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