Proceedings of the American Mathematical Society

A variation of multiple

-values arising from the spectral zeta function of the non-commutative harmonic oscillator

Author(s): Kazufumi Kimoto; Yoshinori Yamasaki
Journal: Proc. Amer. Math. Soc. 137 (2009), 2503-2515.
MSC (2000): Primary 11M41, 05E05; Secondary 11P81, 05A15
Posted: March 24, 2009
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Abstract: A variation of multiple

-values, which arises from the description of the special values of the spectral zeta function of the non-commutative harmonic oscillator, is introduced. In some special cases, we show that its generating function can be written in terms of the gamma functions. This result enables us to obtain explicit evaluations of them.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11M41, 05E05, 11P81, 05A15

Kazufumi Kimoto
Affiliation: Department of Mathematical Sciences, University of the Ryukyus, Senbaru, Nishihara, Okinawa, 903-0231 Japan
Email: kimoto@math.u-ryukyu.ac.jp

Yoshinori Yamasaki
Affiliation: Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812-8581 Japan
Address at time of publication: Graduate School of Science and Engineering, Ehime University, Bunkyo-cho, Matsuyama, 790-8577 Japan
Email: yamasaki@math.sci.ehime-u.ac.jp

DOI: 10.1090/S0002-9939-09-09881-5
PII: S 0002-9939(09)09881-5
Keywords: Multiple zeta values, multiple $L$-values, Bernoulli numbers, non-commutative harmonic oscillator, spectral zeta function, symmetric functions
Received by editor(s): May 8, 2008
Posted: March 24, 2009
Additional Notes: The first author was supported in part by Grant-in-Aid for Young Scientists (B) No. 20740021.
The second author was supported in part by Grant-in-Aid for JSPS Fellows No. 19002485.
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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