Kondo, Hiroki; Saito, Shingo; Tanaka, Tatsushi The Bowman-Bradley theorem for multiple zeta-star values. (English) Zbl 1269.11082 J. Number Theory 132, No. 9, 1984-2002 (2012). Summary: The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of two’s between \(3,1,\ldots ,3,1\) add up to a rational multiple of a power of \(\pi \). We establish its counterpart for multiple zeta-star values by showing an identity in a non-commutative polynomial algebra introduced by Hoffman. Cited in 1 ReviewCited in 5 Documents MSC: 11M32 Multiple Dirichlet series and zeta functions and multizeta values 05A19 Combinatorial identities, bijective combinatorics Keywords:multiple zeta value; multiple zeta-star value; Bowman-Bradley theorem; harmonic algebra PDFBibTeX XMLCite \textit{H. Kondo} et al., J. Number Theory 132, No. 9, 1984--2002 (2012; Zbl 1269.11082) Full Text: DOI arXiv References: [1] Aoki, T.; Kombu, Y.; Ohno, Y., A generating function for sums of multiple zeta values and its applications, Proc. Amer. Math. Soc., 136, 2, 387-395 (2008) · Zbl 1215.11086 [2] Borwein, J. M.; Bradley, D. M.; Broadhurst, D. J.; Lisoněk, P., Combinatorial aspects of multiple zeta values, Electron. J. Combin., 5 (1998), Research paper 38, 12 pp · Zbl 0904.05012 [3] Bowman, D.; Bradley, D. M., The algebra and combinatorics of shuffles and multiple zeta values, J. Combin. Theory Ser. A, 97, 43-61 (2002) · Zbl 1021.11026 [4] Hoffman, M., Multiple harmonic series, Pacific J. Math., 152, 2, 275-290 (1992) · Zbl 0763.11037 [5] Hoffman, M., The algebra of multiple harmonic series, J. Algebra, 194, 2, 477-495 (1997) · Zbl 0881.11067 [6] Imatomi, K.; Tanaka, T.; Tasaka, K.; Wakabayashi, N., On some combinations of multiple zeta-star values [7] Kontsevich, M.; Zagier, D., Periods, (Mathematics Unlimited—2001 and Beyond (2001), Springer: Springer Berlin), 771-808 · Zbl 1039.11002 [8] Muneta, S., On some explicit evaluations of multiple zeta-star values, J. Number Theory, 128, 9, 2538-2548 (2008) · Zbl 1221.11187 [9] Muneta, S., A note on evaluations of multiple zeta values, Proc. Amer. Math. Soc., 137, 3, 931-935 (2009) · Zbl 1180.11031 [10] Ohno, Y.; Zagier, D., Multiple zeta values of fixed weight, depth, and height, Indag. Math. (N.S.), 12, 4, 483-487 (2001) · Zbl 1031.11053 [11] Tanaka, T., A simple proof of certain formula for multiple zeta-star values, J. Algebra Number Theory: Adv. Appl., 3, 2, 97-110 (2010) · Zbl 1306.11068 [12] Yamasaki, Y., Evaluations of multiple Dirichlet \(L\)-values via symmetric functions, J. Number Theory, 129, 10, 2369-2386 (2009) · Zbl 1176.11043 [13] Zlobin, S. A., Generating functions for the values of a multiple zeta function, Vestnik Moskov. Univ. Ser. I Mat. Mekh.. Vestnik Moskov. Univ. Ser. I Mat. Mekh., Moscow Univ. Math. Bull., 60, 2, 44-48 (2005), 73; translation in · Zbl 1101.11036 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.