Schur multiple zeta-functions of Hurwitz type
Kohji Matsumoto, Maki Nakasuji
TL;DR
The paper extends Schur multiple zeta-functions to the Hurwitz-type by introducing $\zeta_{\lambda}({\pmb s}|{\pmb x})$ using shifted arguments in SSYT and relates this to Hurwitz and Euler-Zagier MZFs. It shows that determinant expressions known for ordinary Schur MZF, namely the Jacobi-Trudi and Giambelli formulas, extend to the Hurwitz-type case via content-parametrization and diagonal constraints, with proofs leveraging the Lindström–Gessel–Viennot path framework. It discusses an extended Jacobi-Trudi formula (Nakasuji–Takeda) for certain shapes and notes meromorphic continuation considerations. It also references unpublished results by Yamamoto and Minoguchi and highlights differentiation with respect to shifting parameters as a source of new identities.
Abstract
We study the Hurwitz-type analogue of Schur multiple zeta-functions involving shifting parameters. We extend various formulas, known for ordinary Schur multiple zeta-functions, to the case of Hurwitz type. We also mention unpublished results proved by Yamamoto and by Minoguchi. Further we present new formulas obtained by performing differentiation with respect to shifting parameters.