On special values of Selberg type zeta functions on SU(1, q+1)

Koichi TAKASE

doi:10.2969/jmsj/04340631

Koichi TAKASE

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ジャーナルフリー

1991 年 43 巻 4 号 p. 631-659

DOI https://doi.org/10.2969/jmsj/04340631

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Published: 1991 Received: 1988/08/01 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文受付日訂正内容: 訂正前 : 19890801
訂正後 : 19880801

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : BSB) M. W. Baldoni Silva and D. Barbasch, The unitary spectrum for real rank one groups, Inv. Math., 72 (1983), 27-55.
Dl) P. Deligne, Valeurs de fonctions L et periods d'integrales, Proc. Symp. Pure Math. (Amer. Math. Soc.), 33 (1979), 313-346.
Fr) D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds, Inv. Math., 84 (1986), 523-540.
Gd) R. Godement, A theory of spherical functions I, Trans. Amer. Math. Soc., 73 (1952), 496-556.
GW) R. Gangolli and G.-Warner, On Selberg's trace formula, J. Math. Soc. Japan, 27 (1975), 328-343.
HS) W. Hecht.-Schmidt, On integrable representations of a semi-simple Lie group, Math. Ann., 220 (1976), 147-149.
DP) E. D'Hoker and D. H.-Phong, On determinants of Laplacians on Riemann surfaces, Comm. Math. Phys., 104 (1986), 537-545.
HP) R. Hotta and R. Parthasarathy, Multiplicity formula for discrete series, Inv. Math., 26 (1974), 133-178.
Kr) H. Kraljevic, Representations of the universal covering group of the group SU(n,1), Glasnik Mathemeticki, 8(1973), 22-72.
Mg) W. Magnus, et al., Formulas and theorems for the special functions of mathematical physics, Springer-Verlag, 1960.
Mt) R. Miatello, The Minakshisundaram-Pleijel coefficients for the vector valued heat kernel on compact locally symmetric spaces of negative curvature, Trans. Amer. Math. Soc., 260 (1980), 1-33.
Sh) W. Schmidt, Some properties of square-integrable representations of semi-simple Lie groups, Ann. Math., 102 (1975), 535-564.
Sc) D. Scott, Selberg type zeta functions for the group of complex two by two matrices of determinant one, Math. Ann., 253 (1980), 177-194.
Sl) A. Selberg, Harmonic analysis and discontinuous group in weakly symmetric Riemannian space with application to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87.
Tr) P. C. Trombi, Harmonic analysis of C^p (G; F) (1_??_p<2), J. Functional Analysis, 40 (1988), 84-125.
Vg) M.-F. Vigneras, L'equation fonctionalle de la fonction zeta de Selberg du group modulaire PSL(2,Z), Asterisque, 61 (1979), 235-249.
Vr) A. Voros, Special functions and the Selberg zeta function, Comm. Math. Phys., 110 (1987), 439-465.
Wk1) M. Wakayama, Zeta functions of Selberg's type for compact quotient of SU(n, 1), Hiroshima Math. J., 14 (1984), 597-618.
Wk2) M. Wakayama, Zeta functions of Selberg's type associated with homogeneous vector bundles, Hiroshima Math. J., 15 (1985), 235-295.
Wr) G. Warner, Harmonic analysis on semi-simple Lie groups I, II, Springer-Verlag, 1972.
Wl) A. Weil, Sur les “formules explicates” de la theorie des nombers premiers, Comm. Sem. Math. Univ. de Lund, Medd. Lunds Univ. Math. Sem. Tome supplimentaire (1952), 252-265.

Right : [BSB] M. W. Baldoni Silva and D. Barbasch, The unitary spectrum for real rank one groups, Inv. Math., 72 (1983), 27-55.
[Dl] P. Deligne, Valeurs de fonctions L et periods d'integrales, Proc. Symp. Pure Math. (Amer. Math. Soc.), 33 (1979), 313-346.
[Fr] D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds, Inv. Math., 84 (1986), 523-540.
[Gd] R. Godement, A theory of spherical functions I, Trans. Amer. Math. Soc., 73 (1952), 496-556.
[GW] R. Gangolli and G. -Warner, On Selberg's trace formula, J. Math. Soc. Japan, 27 (1975), 328-343.
[HS] W. Hecht. -Schmidt, On integrable representations of a semi-simple Lie group, Math. Ann., 220 (1976), 147-149.
[DP] E. D'Hoker and D. H. -Phong, On determinants of Laplacians on Riemann surfaces, Comm. Math. Phys., 104 (1986), 537-545.
[HP] R. Hotta and R. Parthasarathy, Multiplicity formula for discrete series, Inv. Math., 26 (1974), 133-178.
[Kr] H. Kraljevic, Representations of the universal covering group of the group SU (n, 1), Glasnik Mathemeticki, 8 (1973), 22-72.
[Mg] W. Magnus, et al., Formulas and theorems for the special functions of mathematical physics, Springer-Verlag, 1960.
[Mt] R. Miatello, The Minakshisundaram-Pleijel coefficients for the vector valued heat kernel on compact locally symmetric spaces of negative curvature, Trans. Amer. Math. Soc., 260 (1980), 1-33.
[Sh] W. Schmidt, Some properties of square-integrable representations of semi-simple Lie groups, Ann. Math., 102 (1975), 535-564.
[Sc] D. Scott, Selberg type zeta functions for the group of complex two by two matrices of determinant one, Math. Ann., 253 (1980), 177-194.
[Sl] A. Selberg, Harmonic analysis and discontinuous group in weakly symmetric Riemannian space with application to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87.
[Tr] P. C. Trombi, Harmonic analysis of C^p (G; F) (1≤p<2), J. Functional Analysis, 40 (1988), 84-125.
[Vg] M. -F. Vigneras, L'equation fonctionalle de la fonction zeta de Selberg du group modulaire PSL (2, Z), Asterisque, 61 (1979), 235-249.
[Vr] A. Voros, Special functions and the Selberg zeta function, Comm. Math. Phys., 110 (1987), 439-465.
[Wk1] M. Wakayama, Zeta functions of Selberg's type for compact quotient of SU (n, 1), Hiroshima Math. J., 14 (1984), 597-618.
[Wk2] M. Wakayama, Zeta functions of Selberg's type associated with homogeneous vector bundles, Hiroshima Math. J., 15 (1985), 235-295.
[Wr] G. Warner, Harmonic analysis on semi-simple Lie groups I, II, Springer-Verlag, 1972.
[Wl] A. Weil, Sur les “formules explicates” de la theorie des nombers premiers, Comm. Sem. Math. Univ. de Lund, Medd. Lunds Univ. Math. Sem. Tome supplimentaire (1952), 252-265.

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