The determinant of the Laplacian on the n-sphere

H. Kumagai

Acta Arithmetica (1999)

  • Volume: 91, Issue: 3, page 199-208
  • ISSN: 0065-1036

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H. Kumagai. "The determinant of the Laplacian on the n-sphere." Acta Arithmetica 91.3 (1999): 199-208. <http://eudml.org/doc/207351>.

@article{H1999,
author = {H. Kumagai},
journal = {Acta Arithmetica},
keywords = {regularized determinant; Hurwitz zeta-function; eigenvalues of the Laplacian; zeta determinant; Laplacian; discrete spectrum; Hurwitz zeta function},
language = {eng},
number = {3},
pages = {199-208},
title = {The determinant of the Laplacian on the n-sphere},
url = {http://eudml.org/doc/207351},
volume = {91},
year = {1999},
}

TY - JOUR
AU - H. Kumagai
TI - The determinant of the Laplacian on the n-sphere
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 3
SP - 199
EP - 208
LA - eng
KW - regularized determinant; Hurwitz zeta-function; eigenvalues of the Laplacian; zeta determinant; Laplacian; discrete spectrum; Hurwitz zeta function
UR - http://eudml.org/doc/207351
ER -

References

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  1. [1] J. S. Choi, Ph.D. thesis, Florida State Univ., 1991. 
  2. [2] J. S. Choi, Determinant of Laplacian on S³, Math. Japon. 40 (1994), 155-166. 
  3. [3] J. S. Choi and H. M. Srivastava, An application of the theory of the double Gamma function, Kyushu J. Math. 53 (1999), 209-222. Zbl1013.11053
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  7. [7] I. Efrat, Determinants of Laplacians on surfaces of finite volume, ibid. 119 (1988), 443-451; erratum, ibid. 138 (1991), 607. Zbl0661.10038
  8. [8] S. Kanemitsu, M. Katsurada and M. Yoshimoto, On the Hurwitz-Lerch zeta function, to appear. Zbl1059.11050
  9. [9] E. Onofri, On the positivity of the effective action in a theory of random surface, Comm. Math. Phys. 86 (1982), 321-326. Zbl0506.47031
  10. [10] B. Osgood, R. Phillips and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), 148-211. Zbl0653.53022
  11. [11] J. R. Quine and J. Choi, Zeta regularized products and functional determinants on spheres, Rocky Mountain J. Math. 26 (1996), 719-729. Zbl0864.47024
  12. [12] P. Sarnak, Determinants of Laplacians, Comm. Math. Phys. 110 (1987), 113-120. Zbl0618.10023
  13. [13] A. Terras, Harmonic Analysis on Symmetric Space and Applications. I, Springer, 1985. 
  14. [14] I. Vardi, Determinants of Laplacians and multiple gamma functions, SIAM J. Math. Anal. 19 (1988), 493-507. Zbl0641.33003
  15. [15] N. Yu. Vilenkin, Special Functions and the Theory of Group Representations, Amer. Math. Soc. Transl. 22, Amer. Math. Soc., 1968, p. 494. 
  16. [16] A. Voros, Spectral functions, special functions and the Selberg zeta function, Comm. Math. Phys. 110 (1987), 439-465. Zbl0631.10025
  17. [17] W. I. Weisberger, Conformal invariants for determinants of Laplacians on Riemann surfaces, ibid. 112 (1987), 633-638. Zbl0629.58031
  18. [18] W. I. Weisberger, Normalization of the path integral measure and the coupling constants for the bosonic strings, Nuclear Phys. B 284 (1987), 171-200. 

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