Analytic continuation of multiple zeta-functions and their values at non-positive integers

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

“…In this lemma, we let α 2l and β 2l be the left-hand side of (5.41) and (5.42) with d = 2l + q for l ∈ N, respectively, and α 0 = β 0 = C −q (1). Note that C 0 (1) is determined by Lemma 5.6, and C −1 (1) = (1/π)L 6 (π; 1; 1) by (5.41).…”

“…Therefore we need to check the cancellation between them. As well as in the proof of Lemma 3.4, we use the technique of "change of variables" introduced in [1]. Put…”

“…Therefore some cancellation between them might occur. In order to check the truth of these singularities, we use the technique of "change of variables" introduced by Akiyama, Egami and Tanigawa ( [1]). Put…”

Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series

“…Zhao [24] independently proved the same fact by a quite different method. Then, using the same technique as in [1], Akiyama and Ishikawa [2] has shown the continuation of (1.20), as mentioned in Section 1. Now we prove the following proposition, which obviously includes the assertion of Theorem 4.…”

“…Next, by using the Euler-Maclaurin summation formula, Akiyama, Egami and Tanigawa [1] proved that (1.21) can be continued to C n as a function of n-variables v 1 , . .…”