On value-relations, functional relations and singularities of Mordell–Tornheim and related triple zeta-functions

Functional relations and special values of Mordell-Tornheim triple zeta and 𝐿-functions

“…Note that the case δ = 1 coincides with the result in [5,Theorem 4.5]. By the same consideration as in the proof of Theorem 3.4 and using Lemma 3.2, we can obtain the following result which can be regarded as a χ-analogue of [5,Theorem 4.5] and as a triple analogue of the recent results about double zeta and L-functions (see [7,8,17,18]).…”

“…Similar to our previous results [3,4,5], this gives the meromorphic continuation of ζ MT,2 (s 1 , s 2 , s 4 ; α, β, 0) and determines its singularities as…”

“…The results in this paper can be regarded as triple analogues of the known results for double zeta and L-functions proved in the papers quoted above and [9,10,13,14,15], and also be regarded as χ-analogues of the results in [5]. Therefore this paper is a step toward the general theory of functional relations for Mordell-Tornheim r-ple zeta and L-functions including known results of r-ple zeta values given in [16].…”

Generalized log sine integrals and the Mordell-Tornheim zeta values

“…There is preceding research [5,23,27,30,31] for the expression of the Mordell-Tornheim zeta function by integrals involving the polylogarithms or associated functions. For other expressions, refer to [11,21,22].…”

On Witten Multiple Zeta-Functions Associated With Semi-Simple Lie Algebras Iv

“…In this section, we quote several lemmas from our previous papers [15,17,7] and further prove an analogue of them. These will play important roles in the next section.…”