@article{bwmeta1.element.bwnjournal-article-aav91i3p199bwm, author = {H. Kumagai}, title = {The determinant of the Laplacian on the n-sphere}, journal = {Acta Arithmetica}, volume = {89}, year = {1999}, pages = {199-208}, zbl = {0946.11021}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav91i3p199bwm} }
H. Kumagai. The determinant of the Laplacian on the n-sphere. Acta Arithmetica, Tome 89 (1999) pp. 199-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav91i3p199bwm/
[000] [1] J. S. Choi, Ph.D. thesis, Florida State Univ., 1991.
[001] [2] J. S. Choi, Determinant of Laplacian on S³, Math. Japon. 40 (1994), 155-166.
[002] [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. | Zbl 1013.11053
[003] [4] L. Comtet, Advanced Combinatorics, Reidel, 1974.
[004] [5] E. D'Hoker and D. H. Phong, Multiloop amplitudes for the bosonic Polyakov string, Nuclear Phys. B 269 (1986), 205-234.
[005] [6] E. D'Hoker and D. H. Phong, On determinants of Laplacians on Riemann surfaces, Comm. Math. Phys. 104 (1986), 537-545.
[006] [7] I. Efrat, Determinants of Laplacians on surfaces of finite volume, ibid. 119 (1988), 443-451; erratum, ibid. 138 (1991), 607. | Zbl 0661.10038
[007] [8] S. Kanemitsu, M. Katsurada and M. Yoshimoto, On the Hurwitz-Lerch zeta function, to appear. | Zbl 1059.11050
[008] [9] E. Onofri, On the positivity of the effective action in a theory of random surface, Comm. Math. Phys. 86 (1982), 321-326. | Zbl 0506.47031
[009] [10] B. Osgood, R. Phillips and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), 148-211. | Zbl 0653.53022
[010] [11] J. R. Quine and J. Choi, Zeta regularized products and functional determinants on spheres, Rocky Mountain J. Math. 26 (1996), 719-729. | Zbl 0864.47024
[011] [12] P. Sarnak, Determinants of Laplacians, Comm. Math. Phys. 110 (1987), 113-120. | Zbl 0618.10023
[012] [13] A. Terras, Harmonic Analysis on Symmetric Space and Applications. I, Springer, 1985.
[013] [14] I. Vardi, Determinants of Laplacians and multiple gamma functions, SIAM J. Math. Anal. 19 (1988), 493-507. | Zbl 0641.33003
[014] [15] N. Yu. Vilenkin, Special Functions and the Theory of Group Representations, Amer. Math. Soc. Transl. 22, Amer. Math. Soc., 1968, p. 494.
[015] [16] A. Voros, Spectral functions, special functions and the Selberg zeta function, Comm. Math. Phys. 110 (1987), 439-465. | Zbl 0631.10025
[016] [17] W. I. Weisberger, Conformal invariants for determinants of Laplacians on Riemann surfaces, ibid. 112 (1987), 633-638. | Zbl 0629.58031
[017] [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.