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

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- by Kazufumi Kimoto and Yoshinori Yamasaki PDF
- Proc. Amer. Math. Soc.
**137**(2009), 2503-2515 Request permission

## 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.## References

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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
- 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
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 2503-2515 - MSC (2000): Primary 11M41, 05E05; Secondary 11P81, 05A15
- DOI: https://doi.org/10.1090/S0002-9939-09-09881-5
- MathSciNet review: 2497462