リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「A Note on Fn-multiple Zeta Values」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

A Note on Fn-multiple Zeta Values

Masataka Ono Kosuke Sakurada Shin-ichiro Seki 立教大学

2021.12.01

概要

For several evaluations of special values and several relations known only in An-multiple zeta values or Sn-multiple zeta values, we prove that they are uniformly valid in Fn-multiple zeta values for both the case where F = A and F = S. In particu- lar, the Bowman–Bradley type theorem and sum formulas for S2-multiple zeta values are proved.

参考文献

[BB] D. Bowman, D. M. Bradley, The algebra and combinatorics of shuffles and multiple zeta values, J. Combin. Theory Ser. A 97 (2002), 43–61.

[HHT] KH. Hessami Pilehrood, T. Hessami Pilehrood, R. Tauraso, New properties of multiple harmonic sums modulo p and p-analogues of Leshchiner’s series, Trans. Amer. Math. Soc. 366 (2014), 3131–3159.

[HMO] M. Hirose, H. Murahara, M. Ono, On variants of symmetric multiple zeta-star values and the cyclic sum formula, Ramanujan J. 56 (2021), 467–489.

[H1] M. E. Hoffman, The algebra of multiple harmonic series, J. Algebra 194 (1997), 477–495.

[H2] M. E. Hoffman, Quasi-symmetric functions and mod p multiple harmonic sums, Kyushu J. Math. 69 (2015), 345–366.

[IKOO] K. Ihara, J. Kajikawa, Y. Ohno, J. Okuda, Multiple zeta values vs. multiple zeta-star values, J. Algebra 332 (2011), 187–208.

[IKZ] K. Ihara, M. Kaneko, D. Zagier, Derivation relation and double shuffle relations for multiple zeta values, Compositio Math. 142 (2006), 307–338.

[J1] D. Jarossay, Double mélange des multizêtas finis et multizêtas symétrisés, C. R. Acad. Sci. Paris, 352 (2014), 767–771.

[J2] D. Jarossay, Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values, preprint, arXiv:1412.5099v5.

[Kan] M. Kaneko, An introduction to classical and finite multiple zeta values, Publications mathématiques de Besançon, no. 1 (2019), 103–129.

[KS] M. Kaneko, M. Sakata, On multiple zeta values of extremal height, Bull. Aust. Math. Soc. 93 (2016), 186–193.

[KZ] M. Kaneko, D. Zagier, Finite multiple zeta values, in preparation.

[Li] Z. Li, Gamma series associated to elements satisfying regularized double shuffle relations, J. Number Theory 130 (2010), 213–231.

[Mun] S. Muneta, A note on evaluations of multiple zeta values, Proc. Amer. Math. Soc. 137 (2009), 931–935. [Mur] H. Murahara, A note on finite real multiple zeta values, Kyushu J. Math. 70 (2016), 197–204.

[MOS] H. Murahara, T. Onozuka, S. Seki, Bowman-Bradley type theorem for finite multiple zeta values in A2, Osaka Journal of Mathematics 57 (2020), 647–653.

[OSY] M. Ono, S. Seki, S. Yamamoto, Truncated t-adic symmetric multiple zeta values and double shuffle relations, Res. number theory 7, 15 (2021).

[Re] C. Reutenauer, Free Lie Algebras, Oxford Science Publications (1993).

[Ro] J. Rosen, Asymptotic relations for truncated multiple zeta values, J. Lond. Math. Soc. (2) 91 (2015), 554–572.

[SW1] S. Saito, N. Wakabayashi, Sum formula for finite multiple zeta values, J. Math. Soc. Japan 67 (2015), 1069–1076.

[SW2] S. Saito, N. Wakabayashi, Bowman-Bradley type theorem for finite multiple zeta values, Tohoku Math. J. (2) 68 (2016), 241–251.

[SS] K. Sakugawa, S. Seki, On functional equations of finite multiple polylogarithms, J. Algebra 469 (2017), 323–357.

[Se] S. Seki, The p-adic duality for the finite star-multiple polylogarithms, Tohoku Math. J. 71 (2019), 111–122.

[SY] S. Seki, S. Yamamoto, Ohno-type identities for multiple harmonic sum, J. Math. Soc. Japan 72 (2020), 673–686.

[Su] Z. H. Sun, Congruences concerning Bernoulli numbers and Bernoulli polynomials, Disc. Appl. Math. 105 (2000), 193–223.

[TT] Y. Takeyama, K. Tasaka, Supercongruences of multiple harmonic q-sums and generalized fi- nite/symmetric multiple zeta values, preprint, arXiv:2012.07067.

[TY] K. Tasaka, S. Yamamoto, On some multiple zeta-star values of one-two-three indices, Int. J. Number Theory 9 (2013), 1171–1184.

[Tau] R. Tauraso, More congruences for central binomial coefficients, J. Number Theory 130 (2010), 2639– 2649.

[W] L. C. Washington, p-adic L-functions and sums of powers, J. Number Theory 69 (1998), 50–61.

[Y] S. Yamamoto, Explicit evaluation of certain sums of multiple zeta-star values, Funct. Approx. Com- ment. Math. 49 (2) (2013), 283–289.

[Z] D. Zagier, Evaluation of the multiple zeta values ζ(2,... , 2, 3, 2,. .., 2), Ann. of Math. 175 (2012), 977–1000.

[ZC] X. Zhou, T. Cai, A generalization of a curious congruence on harmonic sums, Proc. of Amer. Math. Soc. 135 (2007), no. 5, 1329–1333.

[Zh] J. Zhao, Wolstenholme type theorem for multiple harmonic sums, Int. J. Number Theory 4 (2008), 73–106.

参考文献をもっと見る