Mathematical Proceedings of the Cambridge Philosophical Society Asymptotic series for double zeta, double gamma, and Hecke L-functions

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 123, Issue 3, 1998, Pages 385-405

  Matsumoto, Kohji ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85022840222     PISSN: 03050041     EISSN: 14698064     Source Type: Journal    
DOI: 10.1017/s0305004197002168     Document Type: Article

References (24)

1. 8, Dedekind sums, and Hecke L-functions for real quadratic fields. Comment. Math. Univ. St. Pauli 37 (1988), 209-235.
2. T. Abakawa. On special values at s = 0 of partial zeta-functions for real quadratic fields. Osaka J. Math. 31 (1994), 79-94.
3. F. V. Atkinson. The mean-value of the Riemann zeta function, Acta Math. 81 (1949), 353-376.
4. E. W. Babnes. The genesis of the double gamma functions. Proc. London Math. Soc. 31 (1899), 358-381.
5. E. W. Babnes. The theory of the double gamma function. Philos. Trans. Roy. Soc. (A) 196 (1901), 265-387.
6. E. Elizalde, S. D. Odintsov, A. Romeo, A. A. Bytsenk and S. Zerbini. Zeta regularization techniques with applications (World Scientific, 1994).
7. A. ErdElyi et al. (the Bateman manuscript project). Higher transcendental functions Vol. 1 (McGraw-Hill, 1953).
8. M. Katsurada. Asymptotic expansions of the mean values of Dirichlet L-functions II; in Analytic number theory and related topics, K. Nagasaka (ed.) (World Scientific, 1993), pp. 61-71.
9. M. Katsurada. Asymptotic expansions of the mean values of Dirichlet L-functions III. Manuscripta Math. 83 (1994), 425-442.
10. M. Katsurada and K. Matsumoto. Asymptotic expansions of the mean values of Dirichlet L-functions. Math. Z. 208 (1991), 23-39.
11. M. Katsurada and K. Matsumoto. Discrete mean values of Hurwitz zeta-functions. Proc. Japan Acad. 69 A (1993), 164-169.
12. M. Katsurada and K. Matsumoto. Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions. Proc. Japan Acad. 303-307.
13. M. Katsurada and K. Matsumoto. The mean values of Dirichlet L-functions at integer points and class numbers of cyclotomic fields. Nagoya Math. J. 134 (1994), 151-172.
14. M. Katsurada and K. Matsumoto. Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions I. Math. Scand., 78 (1996), 161-177.
15. M. MikolAs. Mellinsche Transformation und Orthogonalitat bei (s, u); Verallgemeinerung der Riemannschen Funktionalgleichung von (s). Acta Sci. Math. Szeged 17 (1956), 143-164.
16. Y. Motohashi. A note on the mean value of the zeta and L-functions I. Proc. Japan Acad. 61 (1985), 222-224.
17. P. Sarnak. Determinants of Laplacians. Commun. Math. Phys. 110 (1987), 113-120.
18. T. Shintani. On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), 393-417.
19. T. Shintani. On a Kronecker limit formula for real quadratic fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), 167-199.
20. T. Shintani. A proof of the classical Kronecker limit formula. Tokyo J. Math. 3 (1980), 191-199.
21. E. C. Titchmarsh. The theory of the Riemann zeta-function (Oxford, 1951).
22. I. Vardi. Determinants of Laplacians and multiple gamma functions. SIAM J. Math. Anal. 19 (1988), 493-507.
23. A. Voros. Spectral functions, special functions and the Selberg zeta function. Comm. Math. Phys. 110 (1987), 439-465.
24. E. T. Whittaker and G. N. Watson. A course of modern analysis, 4th ed. (Cambridge University Press, 1927).