Zeta and L-functions and Bernoulli polynomials of root systems

Proceedings of the Japan Academy Series A: Mathematical Sciences

Volumn 84, Issue 5, 2008, Pages 57-62

  Komori, Yasushi ^a   Matsumoto, Kohji ^a   Tsumura, Hirofumi ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

Analytic continuation; Functional relation; Multiple zeta function; Root systems; Simple Lie algeras; Witten zeta function

Indexed keywords

EID: 44449083461     PISSN: 03862194     EISSN: None     Source Type: Journal    
DOI: 10.3792/pjaa.84.57     Document Type: Article

References (21)

1. T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York, 1976.
2. P. E. Gunnells and R. Sczech, Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions, Duke Math. J. 118 (2003), 229-260.
3. J. E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972.
4. J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge Univ. Press, Cambridge, 1990.
5. Y. Komori, K. Matsumoto and H. Tsumura, Zeta-functions of root systems, in "Proceedings of the Conference on L-functions" (Fukuoka, 2006), L. Weng and M. Kaneko (eds), World Scientific, 2007, pp. 115-140.
6. Y. Komori, K. Matsumoto and H. Tsumura, Zeta-functions of root systems, their functional relations, and Dynkin diagrams, in 'Analytic Number Theory' (Kyoto, 2006), RIMS Kokyuroku. (to appear).
7. Y. Komori, K. Matsumoto and H. Tsumura, On Witten multiple zeta-functions associated with semisimple Lie algebras II. (Preprint).
8. Y. Komori, K. Matsumoto and H. Tsumura, On Witten multiple zeta-functions associated with semisimple Lie algebras III. (Preprint).
9. Y. Komori, K. Matsumoto and H. Tsumura, On multiple Bernoulli polynomials and multiple L-functions of root systems. (Preprint).
10. Y. Komori, K. Matsumoto and H. Tsumura, On Witten multiple zeta-functions associated with semisimple Lie algebras IV. (in preparation).
11. K. Matsumoto, Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series, Nagoya Math J. 172 (2003), 59-102.
12. K. Matsumoto, On the analytic continuation of various multiple zeta-functions, in Number theory for the millennium, II (Urbana, IL, 2000), 417-440, A K Peters, Natick, MA.
13. K. Matsumoto, The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions I, J. Number Theory 101 (2003), 223-243.
14. K. Matsumoto, On Mordell-Tornheim and other multiple zeta-functions, in 'Proceedings of the Session in analytic number theory and Diophantine equations' (Bonn, January-June 2002), D. R. Heath-Brown and B. Z. Moroz (eds.), Bonner Mathematische Schriften Nr. 360, Bonn 2003, n.25, 17pp.
15. K. Matsumoto and H. Tsumura, On Witten multiple zeta-functions associated with semi-simple Lie algebras I, Ann. Inst. Fourier (Grenoble) 56 (2006), no. 5, 1457-1504.
16. K. Matsumoto and H. Tsumura, Functional relations for various multiple zeta-functions, in 'Analytic Number Theory' (Kyoto, 2005), RIMS Kokyuroku No. 1512 (2006), 179-190.
17. T. Nakamura, Double L-value relations and functional relations for Witten zeta functions, Tokyo J. Math, (to appear).
18. H. Tsumura, On some functional relations between Mordell-Tornheim double L-functions and Dirichlet L-functions, J. Number Theory 120 (2006), no. 1, 161-178.
19. H. Tsumura, On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 3, 395-405.
20. E. Witten, On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), no. 1, 153-209.
21. D. Zagier, Values of zeta functions and their applications, in First European Congress of Mathematics, Vol. II (Paris, 1992), 497-512, Progr. Math., 120, Birkhäuser, Basel, 1994.