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INTERPOLATED SCHUR MULTIPLE ZETA VALUES

Part of: Graph theory Algebraic combinatorics Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  25 October 2017

HENRIK BACHMANN Open the ORCID record for HENRIK BACHMANN [Opens in a new window]
HENRIK BACHMANN*
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Furo-cho, Nagoya 464-8602, Japan email henrik.bachmann@math.nagoya-u.ac.jp
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Abstract

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Inspired by the recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki, we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values. Our main result will be a Jacobi–Trudi formula for a certain class of these new objects. This generalizes an analogous result for Schur multiple zeta values and implies algebraic relations between interpolated multiple zeta values.

Keywords

multiple zeta valuesSchur functionsJacobi–Trudi formulainterpolated multiple zeta values

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 05E05: Symmetric functions and generalizations 05C30: Enumeration in graph theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 104 , Issue 3 , June 2018 , pp. 289 - 307
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Aigner, M. and Ziegler, G., Proofs from the Book, 5th edn (Springer, Berlin, 2014).Google Scholar
Nakasuji, M., Phuksuwan, O. and Yamasaki, Y., ‘On Schur multiple zeta functions: a combinatoric generalization of multiple zeta functions’, Preprint, 2017, arXiv:1704.08511 [math.NT].Google Scholar
Wakabayashi, N., ‘Interpolation of q-analogue of multiple zeta and zeta-star values’, J. Number Theory 174 (2017), 26–39.Google Scholar
Yamamoto, S., ‘Interpolation of multiple zeta and zeta-star values’, J. Algebra 385 (2013), 102–114.Google Scholar