# 臺灣博碩士論文加值系統

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 For multiple zeta values and multiple zeta-star values, we are interested in some Q-linear relations with fixed weight and fixed length. One of these relations we will probe is the so-called cyclic sum forumlas. Specially, the cyclic equivalence classes of multiple zeta-star values are inclued in this thesis.
 Acknowledgements iiAbstract iv1 Introduction 12 Algebra of Multiple Zeta Values 33 Relations between MZVs and MZSVs 64 Cyclic Sum Formulas 8References 20
 [1] T. Aoki and Y. Ohno, Sum relations for multiple zeta values and connection formulas for Gauss hypergeometric functions, Publ. RIMS, Kyoto Univ., 41 (2005), no. 2, 329-337.[2] R. Apéry, Irrationalité, Astérisque, 61 (1979), 11-13.[3] V. G. Drinfel'd, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(Q bar/Q). (Russian) Algebra i Analiz 2 (1990), no. 4, 149-181; translation in Leningrad Math. J. 2 (1991), no. 4, 829-860.[4] M. Eie, W.-C. Liaw, and Y. L. Ong, A restricted sum formula among multiple zeta values, J. Number Theory 129 (2009), no. 4, 908-921.[5] M. Eie, W.-C. Liaw, and F.-Y. Yang, On evaluation of generalized Euler sums of even weight, Int. J. Number Theory 1 (2005), no. 2, 225-242.[6] L. Guo and B. Xie, Weighted sum formula for multiple zeta values, J. Number Theory 129 (2009), no. 11, 2747-2765.[7] M. E. Hoffman, Multiple harmonic series, Paci c J. Math. 152 (1992), no. 2, 275-290.[8] M. E. Hoffman, The algebra of multiple harmonic series, J. Algebra 194 (1997), no. 2, 477-495.[9] M. E. Hoffman, Algebraic aspects of multiple zeta values, Dev. Math. 14, Springer, 2005, 51-73.[10] M. E. Hoffman and Y. Ohno, Relations of multiple zeta values and their algebraic expression, J. Algebra 262 (2003), no. 2, 332-347.[11] K. Ihara, J. Kajikawa, Y. Ohno, J. Okuda, Multiple Zeta Values vs. multiple zetastar values, J. Algebra 332 (2011), no. 1, 187-208.[12] K. Ihara, M. Kaneko , and D. Zagier, Derivation and double shue relation for multiple zeta values, Compos. Math. 142 (2006), no. 2, 307-338.[13] G. Kawashima, A class of relations among multiple zeta values, J. Number Theory 129 (2009), no. 4, 755-788.[14] Y. Ohno, A generalization of duality and sum formulas on the multiple zeta values, J. Number Theory 74 (1999), no. 1, 39-43.[15] Y. Ohno and N. Wakabayashi, Cyclic sum of multiple zeta values, Acta Arith. 123 (2006), no. 3, 289-295.[16] Y. Ohno and W. Zudilin, Zeta star, Commun. Number Theory Phys. 2 (2008), no.2, 325-347.[17] T. Rivoal, Irrationality of in nitely many values of the zeta function at odd integers, C. R. Acad. Sci. Paris Sér. I Math. 331 (2001), no. 4, 267-270.[18] G.-C. Rota, B. Sagan, and P. R. Stein, A cyclic derivative in noncommutative algebra, J. Algebra 64 (1980), no. 1, 54-75.[19] T. Tanaka and N. Wakabayashi, An algebraic proof of the cyclic sum formula for multiple zeta values, J. Number Theory 323 (2010), no. 3, 766-778.[20] D. Zagier, Values of zeta functions and their applications, First European Congress of Mathematics, Birkhäuser, Boston, 1994, pp. 497-512.[21] V. V. Zudilin, Algebraic relations for multiple zeta values, Uspekhi Mat. Nauk 58(2003), 3-32; translation in Russian Math. Surveys 58 (2003), no. 1, 1-29.
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