Details
| Original language | English |
|---|---|
| Pages (from-to) | 64-88 |
| Number of pages | 25 |
| Journal | Journal of geometry and physics |
| Volume | 58 |
| Issue number | 1 |
| Publication status | Published - 22 Sept 2007 |
| Externally published | Yes |
Abstract
We derive the spectral zeta function in terms of certain Dirichlet series for a variety of spherical space forms MG. Extending results in [C. Nash, D. O'Connor, Determinants of Laplacians on lens spaces, J. Math. Phys. 36 (3) (1995) 1462-1505] the zeta-regularized determinant of the Laplacian on MG is obtained explicitly from these formulas. In particular, our method applies to manifolds of dimension higher than 3 and it includes the case where G arises from the dihedral group of order 2 m. As a crucial ingredient in our analysis we determine the dimension of eigenspaces of the Laplacian in form of some combinatorial quantities for various infinite classes of manifolds from the explicit form of the generating function in [A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math. 17 (1980) 75-93].
Keywords
- Generating function, Hurwitz zeta function, Lens space, Spectral zeta function, Spherical space form, Zeta regularized determinant
ASJC Scopus subject areas
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Mathematics(all)
- Geometry and Topology
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In: Journal of geometry and physics, Vol. 58, No. 1, 22.09.2007, p. 64-88.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Zeta regularized determinant of the Laplacian for classes of spherical space forms
AU - Bauer, W.
AU - Furutani, K.
N1 - Funding Information: Both authors are partially supported by the Grant-in-aid Scientific Research (C) (No. 17540202), Japan Society for the Promotion of Science. Copyright: Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2007/9/22
Y1 - 2007/9/22
N2 - We derive the spectral zeta function in terms of certain Dirichlet series for a variety of spherical space forms MG. Extending results in [C. Nash, D. O'Connor, Determinants of Laplacians on lens spaces, J. Math. Phys. 36 (3) (1995) 1462-1505] the zeta-regularized determinant of the Laplacian on MG is obtained explicitly from these formulas. In particular, our method applies to manifolds of dimension higher than 3 and it includes the case where G arises from the dihedral group of order 2 m. As a crucial ingredient in our analysis we determine the dimension of eigenspaces of the Laplacian in form of some combinatorial quantities for various infinite classes of manifolds from the explicit form of the generating function in [A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math. 17 (1980) 75-93].
AB - We derive the spectral zeta function in terms of certain Dirichlet series for a variety of spherical space forms MG. Extending results in [C. Nash, D. O'Connor, Determinants of Laplacians on lens spaces, J. Math. Phys. 36 (3) (1995) 1462-1505] the zeta-regularized determinant of the Laplacian on MG is obtained explicitly from these formulas. In particular, our method applies to manifolds of dimension higher than 3 and it includes the case where G arises from the dihedral group of order 2 m. As a crucial ingredient in our analysis we determine the dimension of eigenspaces of the Laplacian in form of some combinatorial quantities for various infinite classes of manifolds from the explicit form of the generating function in [A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math. 17 (1980) 75-93].
KW - Generating function
KW - Hurwitz zeta function
KW - Lens space
KW - Spectral zeta function
KW - Spherical space form
KW - Zeta regularized determinant
UR - http://www.scopus.com/inward/record.url?scp=37349081959&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2007.09.007
DO - 10.1016/j.geomphys.2007.09.007
M3 - Article
AN - SCOPUS:37349081959
VL - 58
SP - 64
EP - 88
JO - Journal of geometry and physics
JF - Journal of geometry and physics
SN - 0393-0440
IS - 1
ER -