Multiple gamma functions and multiple q-gamma functions

Publications of the Research Institute for Mathematical Sciences

Volumn 33, Issue 5, 1997, Pages 813-838

  Ueno, Kimio ^a   Nishizawa, Michitomo ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22044455779     PISSN: 00345318     EISSN: 16634926     Source Type: Journal    
DOI: 10.2977/prims/1195145019     Document Type: Article

References (26)

1. Askey, R., The q-Gamma and q-Beta functions, Appl. Anal., 8(1978), 125-141.
2. Barnes, E. W., The theory of G-function, Quat. J. Math., 31 (1899), 261-314.
3. _, Genesis of the double gamma function, Proc. London Math. Soc., 31 (1900), 358-381.
4. _, The theory of the double gamma function, Phil. Trans. Royal. Soc. (A), 196 (1900), 265-388.
5. _, On the theory of the multiple gamma functions, Trans. Cambridge Phil. Soc., 19 (1904), 374-425.
6. Dufresnoy, J. et Pisot, C., Sur la relation fanctionalle f(x + 1) - f(x) = φ(x), Bull. Soc. Math. Belgique, 15 (1963), 259-270.
7. Hardy, G. H., On the expression of the double zeta-function and double gamma function in terms of elliptic functions, Trans. Cambridge. Phil. Soc., 20 (1905), 395-427.
8. _, On double Fourier series and especially these which represent the double zeta-function and incommensurable parameters, Quart. J. Math., 37 (1906), 53-79.
9. n, Proc. Roy. Soc. London, 74 (1904), 64-72.
10. Jackson, F. H., The basic gamma function and the elliptic functions, Proc. Roy. Soc. London, A76 (1905), 127-144.
11. Koornwinder, T., Jacobi function as limit cases of q-ultraspherical polynomial, J. Math. Anal. Appl., 148 (1990), 44-54.
12. Kurokawa, N., Multiple sine functions and Selberg zeta functions, Proc. Japan Acad., 67A (1991), 61-64.
13. _, Multiple zeta functions; an example, Adv. Stud. Pure Math., 21 (1992), 219-226.
14. _, Gamma factors and Plancherel measures, Proc. Japan Acad., 68A (1992), 256-260.
15. _, On a q-analogues of multiple sine functions, RIMS, Kokyuroku, 843 (1992), 1-10.
16. Kurokawa, N., Lectures delivered at Tokyo Institute of Technology, 1993.
17. Manin, Yu., Lectures on Zeta Functions and Motives, Asterisque, 228 (1995), 121-163.
18. Moak, D. S., The q-analogue of Stirling Formula, Rocky Mountain J. Math., 14 (1984), 403-413.
19. Nishizawa, M., On a q-analogue of the multiple gamma functions, Lett. Math. Phys., 37 (1996), 201-209, q-alg/9505086.
20. Shintani, T., On a Kronecker limit formula for real quadratic fields, J. Fac. Sci. Univ. Tokyo Sect. 1A, 24 (1977), 167-199.
21. _, A proof of Classical Kronecker limit formula, Tokyo J. Math., 3 (1980), 191-199.
22. Ueno, K. and Nishizawa, M., Quantum groups and zeta-functions, in: J. Lukierski, Z. Popowicz and J. Sobczyk (eds.) 'Quantum Groups: Formalism and Applications" Proceedings of the XXX-th Karpacz Winter School. 115-126, Polish Scientific Publishers PWN.
23. Vardi, I., Determinants of Laplacians and multiple gamma functions, SIAM. J. Math. Anal., 19 (1988), 493-507.
24. Vignéras, M. F., L'équation fonctionalie de la fonction zeta de Selberg de groupe modulaire PSL(2, Z), Asterisque, 61 (1979), 235-249.
25. Voros, A., Spectral functions, Special functions and the Selberg zeta functions, Comm. Math. Phys., 110 (1987), 431-465.
26. Whittacker, E. T. and Watson, G. N., A Course of Modern Analysis, Fourth edition, Cambrige Univ. Press, 1927.