Generalized multiple Dirichlet series and generalized multiple polylogarithms

On Witten multiple zeta-functions associated with semisimple Lie algebras I

“…Note that we have already considered F 2 (t; s; u) in the case when each s j ∈ N in [21]. We can prove the following lemma by the same method as in the proof of Theorem 1.3 and Proposition 2.1 in [16]. This lemma can also be regarded as a double analogue of Lemma 5.1.…”

“…We quote some notation and results from [16,21,24]. Throughout this section we fix a small δ ∈ R with δ > 0.…”

“…-We consider the well-known contour integrals (see, for example, [16] Proof of Proposition 2.1) as follows. Let Υ be the path which consists of the positive real axis [ε, ∞] (top side), a circle C ε around 0 of radius ε, and the positive real axis [ε, ∞] (bottom side), where 0 < ε < π.…”

On certain polylogarithmic double series

“…We recall the results in [15,17] (see also [10]) in order to make use of them. Throughout this paper we fix a small δ ∈ R with δ > 0.…”

“…The author also wishes to express his sincere gratitude to Professor Kohji Matsumoto for his valuable comments on the analytic theory of zeta-functions. For more general types of multiple polylogarithms, we refer to the joint paper with him and the author [10].…”