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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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