A formula for the logarithmic derivative of Selberg's zeta function

Masato WAKAYAMA

doi:10.2969/jmsj/04130463

Masato WAKAYAMA

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1989 Volume 41 Issue 3 Pages 463-471

DOI https://doi.org/10.2969/jmsj/04130463

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Published: 1989 Received: December 07, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) D. Fried, The zeta functions of Ruelle and Selberg I, Ann. Sci. École Norm. Sup., 4^e série, t. 19 (1986), 491-517.
2) R. Gangolli, Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one, Illinois J. Math., 21 (1977), 1-41.
3) R. Gangolli, On the length spectra of certain compact manifolds of negative curvature, J. Duff. Geom., 12 (1977), 403-423.
4) D. Hejhal, The Selberg trace formula and the Riemann zeta function, Duke Math. J., 43 (1976), 441-482.
5) D. Hejhal, The Selberg Trace Formula for PSL(2, R), Vol. I, Lecture Notes in Math., 548, Springer, 1976.
6) M. Kuga, Topological analysis and its applications in weakly symmetric Riemannian spaces, Sûgaku, 9 (1958), 166-185, (Japanese).
7) B. Randol, Small eigenvalues of the Laplace operator on compact Riemann surfaces, Bull. Amer. Math. Soc., 80 (1974), 996-1000.
8) A. Selberg, Harmonic analysis and discontinuous subgroups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87.
9) M. Wakayama, Zeta functions of Selberg's type for compact quotient of SU(n, 1) (n_??_2), Hiroshima Math. J., 14 (1984), 597-618.
10) M. Wakayama, Zeta functions of Selberg's type associated with homogeneous vector bundles, Hiroshima Math. J., 15 (1985), 235-295.
11) N. Wallach, An asymptotic formula of Gelfand and Gangolli for the spectrum of Γ_??_G, J. Duff. Geom., 11 (1976), 91-101.
12) G. Warner, Harmonic Analysis on Semi-Simple Lie Groups, I, II, Springer, 1972.
13) F. Whittaker and G. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, London/New York, 1927.

Right : [1] D. Fried, The zeta functions of Ruelle and Selberg I, Ann. Sci. École Norm. Sup., 4^e série, t. 19 (1986), 491-517.
[2] R. Gangolli, Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one, Illinois J. Math., 21 (1977), 1-41.
[3] R. Gangolli, On the length spectra of certain compact manifolds of negative curvature, J. Duff. Geom., 12 (1977), 403-423.
[4] D. Hejhal, The Selberg trace formula and the Riemann zeta function, Duke Math. J., 43 (1976), 441-482.
[5] D. Hejhal, The Selberg Trace Formula for PSL(2,R), Vol. I, Lecture Notes in Math., 548, Springer, 1976.
[6] M. Kuga, Topological analysis and its applications in weakly symmetric Riemannian spaces, Sûgaku, 9 (1958), 166-185, (Japanese).
[7] B. Randol, Small eigenvalues of the Laplace operator on compact Riemann surfaces, Bull. Amer. Math. Soc., 80 (1974), 996-1000.
[8] A. Selberg, Harmonic analysis and discontinuous subgroups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87.
[9] M. Wakayama, Zeta functions of Selberg's type for compact quotient of SU(n,1) (n≥2), Hiroshima Math. J., 14 (1984), 597-618.
[10] M. Wakayama, Zeta functions of Selberg's type associated with homogeneous vector bundles, Hiroshima Math. J., 15 (1985), 235-295.
[11] N. Wallach, An asymptotic formula of Gelfand and Gangolli for the spectrum of Γ_??_G, J. Duff. Geom., 11 (1976), 91-101.
[12] G. Warner, Harmonic Analysis on Semi-Simple Lie Groups, I, II, Springer, 1972.
[13] F. Whittaker and G. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, London/New York, 1927.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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