Checkerboard style Schur multiple zeta values and odd single zeta values

We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes, filled with alternating entries like a Checkerboard. In partic...

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Veröffentlicht in:Mathematische Zeitschrift 2018-12, Vol.290 (3-4), p.1173-1197
Hauptverfasser: Bachmann, Henrik, Yamasaki, Yoshinori
Format: Artikel
Sprache:eng
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Zusammenfassung:We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes, filled with alternating entries like a Checkerboard. In particular we obtain new sum representation for odd single zeta values in terms of these Schur multiple zeta values. As a special case we show that some Schur multiple zeta values of Checkerboard style, filled with 1 and 3, are given by determinants of matrices with odd single zeta values as entries.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-018-2058-5