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Zeta function determinant of the Laplace operator on theD-dimensional ball

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Abstract

We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for any value of the dimension,D, of the ball, can be obtained quite easily. Explicit results are presented here for dimensionsD=2,3,4,5 and 6.

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Author notes

  1. E. Elizalde

    Present address: Departament d'ECM and IFAE, Facultat de Física, Universitat de Barcelona, Av. Diagonal 647, E-08028, Barcelona, Spain

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10, D-04109, Leipzig, Germany

    M. Bordag, B. Geyer & K. Kirsten

  2. CSIC, CEAB, Camí de Santa Bàrbara, 17300, Blanes

    E. Elizalde

Authors
  1. M. Bordag
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  2. B. Geyer
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  3. K. Kirsten
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  4. E. Elizalde
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Additional information

Communicated by R.H. Dijkgraaf

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Bordag, M., Geyer, B., Kirsten, K. et al. Zeta function determinant of the Laplace operator on theD-dimensional ball. Commun.Math. Phys. 179, 215–234 (1996). https://doi.org/10.1007/BF02103720

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  • DOI: https://doi.org/10.1007/BF02103720

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