Kodai Mathematical Journal

Spectral zeta functions for compact symmetric spaces of rank one

Akira Ikeda

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 23, Number 3 (2000), 345-357.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138044263

Digital Object Identifier
doi:10.2996/kmj/1138044263

Mathematical Reviews number (MathSciNet)
MR1787669

Zentralblatt MATH identifier
1018.58024

Subjects
Primary: 58J52: Determinants and determinant bundles, analytic torsion
Secondary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}

Citation

Ikeda, Akira. Spectral zeta functions for compact symmetric spaces of rank one. Kodai Math. J. 23 (2000), no. 3, 345--357. doi:10.2996/kmj/1138044263. https://projecteuclid.org/euclid.kmj/1138044263


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References

  • [1] M. BERGER, P GAUDUCHON AND E. MAZET, Le Spectre d'une Variete Riemannianne, Lecture Notes in Math., 194, Springer-Verlag, Berlin, 1971.
  • [2] R. S. CAHN AND J. A. WOLF, Zeta functions and their asymptotic expansions for compac symmetric spaces of rank one, Comment. Math. Helv., 51 (1976), 1-21.
  • [3] E. CARLETTI AND G. MONTI BRAGARDIN, On Dichlet series associated with polynomials, Proc. Amer. Math. Soc, 121 (1994), 33-3
  • [4] E. CARLETTI AND G. MONTI BRAGARDIN, On Minakshisundaram-Pleijel zeta functions o spheres, Proc. Amer. Math. Soc, 122 (1994), 993-1001.
  • [5] M. Em, On a Dinchlet series associated with Polynomial, Proc. Amer. Math. Soc, 11 (1990), 583-590.
  • [6] P. GILKEY, Invanance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, 2nd ed., CRC Press, 1994
  • [7] A. IKEDA ANDY TANIGUCHI, Spectra and eigenforms of the Laplacian on Sn and Pn(C), Osaka J. Math, 15 (1978), 515-546
  • [8] A. IKEDA, Zeta functions for differential forms on standard spheres and their asymptoti expansions, Bull. Fac School Edu. Hiroshima Univ. Part II, 11 (1988), 31-40.
  • [9] S. MINAKSHISUNDARAM AND A. PLEIJEL, Some properties of the eigenvalues of the Laplac operator on Riemanman manifolds, Canad. J. Math, 1 (1949), 242-256.
  • [10] S. MINAKSHISUNDARAM, Zeta functions on the spheres, J. Indian Math. Soc, 13 (1949), 41 48.
  • [11] R. SUNADA, Fundamental groups and Laplacian, Kinokuniya, Tokyo, 1988 (in Japanese)
  • [12] E. T. WHTTTAKER AND G. N. WATSON, Modern Analysis, Cambridge Univ. Press, London, 1958