Analytic continuation of multiple zeta-functions and their values at non-positive integers

Acta Arithmetica

Volumn 98, Issue 2, 2001, Pages 107-116

  Akiyama, Shigeki ^a   Egami, Shigeki ^c   Tanigawa, Yoshio ^b  

^a NIIGATA UNIVERSITY   (Japan)

^b NAGOYA UNIVERSITY   (Japan)

^c UNIVERSITY OF TOYAMA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035651776     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa98-2-1     Document Type: Article

References (21)

1. S. Akiyama and H. Ishikawa, An analytic continuation of multiple L-functions and related zeta-functions, in: Analytic Number Theory, C. Jia and K. Matsumoto (eds.), to appear.
2. S. Akiyama and Y. Tanigawa, Multiple zeta values at non-positive integers, submitted.
3. T. M. Apostol, Introduction to Analytic Number Theory, Springer, 1976.
4. T. Arakawa and M. Kaneko, Multiple zeta values, poly-Bernoulli numbers, and related zeta-functions, Nagoya Math. J. 153 (1999), 189-209.
5. F. V. Atkinson, The mean value of the Riemann zeta-function, Acta Math. 81 (1949), 353-376.
6. J. M. Borwein, D. M. Bradley, D. J. Broadhurst and P. Lisoněk, Combinatorial aspects of multiple zeta values, Electron. J. Combin. 5 (1998), no. 1, Research Paper 38, 12 pp.
7. D. J. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B 393 (1997), 403-412.
8. H. M. Edwards, Riemann's Zeta Function, Academic Press, New York, 1974.
9. S. Egami, Reciprocity laws of multiple zeta functions and generalized Dedekind sums, in: Analytic Number Theory and Related Topics (Tokyo, 1991), World Sci., River Edge, NJ, 1993, 17-27.
10. -, Introduction to multiple zeta function, lecture notes at Niigata Univ. (in Japanese); DVI and TeX files available at http://mathalg.ge.niigata-u.ac.jp/Seminar/Intensive/Egami.html.
11. R. C. Gunning, Introduction to Holomorphic Functions of Several Variables II, Wadsworth & Brooks/Cole, 1990.
12. A. Ivić, The Riemann Zeta-Function, Wiley, New York, 1985.
13. M. Katsurada and K. Matsumoto, Asymptotic expansions of the mean values of Dirichlet L-functions, Math. Z. 208 (1991), 23-39.
14. T. Q. T. Le and J. Murakami, Kontsevich's integral for the Homfly polynomial and relations between values of multiple zeta functions, Topology Appl. 62 (1995), 193-206.
15. Y. Motohashi, A note on the mean value of the zeta and L-functions. I, Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), 222-224.
16. Y. Ohno, A generalization of the duality and sum formulas on the multiple zeta values, J. Number Theory 74 (1999), 39-43.
17. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed. (revised by D. R. Heath-Brown), Clarendon Press, Oxford, 1986.
18. D. Zagier, Values of zeta-functions and their applications, in: First European Congress of Mathematics, Vol. II, Birkhäuser, 1994, 497-512.
19. -, Periods of modular forms, traces of Hecke operators, and multiple zeta values, in: Research into Automorphic Forms and L Functions (Kyoto, 1992), Sūrikaisekikenkyūsho Kōkyūroku 843 (1993), 162-170 (in Japanese).
20. -, Periods of modular forms, traces of Hecke operators, and multiple zeta values, in: Research into Automorphic Forms and L Functions (Kyoto, 1992), Sūrikaisekikenkyūsho Kōkyūroku 843 (1993), 162-170 (in Japanese).
21. J. Q. Zhao, Analytic continuation of multiple zeta function, Proc. Amer. Math. Soc. 128 (2000), 1275-1283.