2024-03-29T07:17:10Z
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2023-01-16T04:43:15Z
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On Witten multiple zeta-functions associated with semisimple Lie algebras I
Sur les fonctions zeta multiples de Witten associées aux algèbres de Lie semi-simples
Matsumoto, Kohji
Tsumura, Hirofumi
open access
Witten multiple zeta-functions
Mordell-Tornheim zeta-functions
Riemann zeta-function
analytic continuation
semisimple Lie algebra
We define Witten multiple zeta-functions associated with semisimple Lie algebras sl(n), (n=2,3,...) of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case sl(4), we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations, we prove new and non-trivial evaluation formulas for special values of this function at positive integers.
Annales de L'Institut Fourier
2006
eng
journal article
VoR
http://hdl.handle.net/2237/20336
https://nagoya.repo.nii.ac.jp/records/17981
https://doi.org/10.5802/aif.2218
1777-5310
Annales de l'institut Fourier
56
5
1457
1504
https://nagoya.repo.nii.ac.jp/record/17981/files/40.pdf
application/pdf
565.9 kB
2018-02-21