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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A variation of multiple $ L$-values arising from the spectral zeta function of the non-commutative harmonic oscillator


Authors: Kazufumi Kimoto and Yoshinori Yamasaki
Journal: Proc. Amer. Math. Soc. 137 (2009), 2503-2515
MSC (2000): Primary 11M41, 05E05; Secondary 11P81, 05A15
Published electronically: March 24, 2009
MathSciNet review: 2497462
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Abstract: A variation of multiple $ L$-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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Additional Information

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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.