The determinant of the Laplacian on the n-sphere

• Autorzy: H. Kumagai
• Języki publikacji: EN

Słowa kluczowe

EN

regularized determinant; Hurwitz zeta-function; eigenvalues of the Laplacian

Kategorie tematyczne

• 11M41: Other Dirichlet series and zeta functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 91
• Numer: 3
• Strony: 199-208

Daty

wydano

1999

otrzymano

1997-07-18

poprawiono

1999-05-12

Twórcy

autor

H. Kumagai

• Department of Electrical Engineering, University of Kinki, Iizuka, Fukuoka 820-8555, Japan

Bibliografia

• [1] J. S. Choi, Ph.D. thesis, Florida State Univ., 1991.
• [2] J. S. Choi, Determinant of Laplacian on S³, Math. Japon. 40 (1994), 155-166.
• [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.
• [4] L. Comtet, Advanced Combinatorics, Reidel, 1974.
• [5] E. D'Hoker and D. H. Phong, Multiloop amplitudes for the bosonic Polyakov string, Nuclear Phys. B 269 (1986), 205-234.
• [6] E. D'Hoker and D. H. Phong, On determinants of Laplacians on Riemann surfaces, Comm. Math. Phys. 104 (1986), 537-545.
• [7] I. Efrat, Determinants of Laplacians on surfaces of finite volume, ibid. 119 (1988), 443-451; erratum, ibid. 138 (1991), 607.
• [8] S. Kanemitsu, M. Katsurada and M. Yoshimoto, On the Hurwitz-Lerch zeta function, to appear.
• [9] E. Onofri, On the positivity of the effective action in a theory of random surface, Comm. Math. Phys. 86 (1982), 321-326.
• [10] B. Osgood, R. Phillips and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), 148-211.
• [11] J. R. Quine and J. Choi, Zeta regularized products and functional determinants on spheres, Rocky Mountain J. Math. 26 (1996), 719-729.
• [12] P. Sarnak, Determinants of Laplacians, Comm. Math. Phys. 110 (1987), 113-120.
• [13] A. Terras, Harmonic Analysis on Symmetric Space and Applications. I, Springer, 1985.
• [14] I. Vardi, Determinants of Laplacians and multiple gamma functions, SIAM J. Math. Anal. 19 (1988), 493-507.
• [15] N. Yu. Vilenkin, Special Functions and the Theory of Group Representations, Amer. Math. Soc. Transl. 22, Amer. Math. Soc., 1968, p. 494.
• [16] A. Voros, Spectral functions, special functions and the Selberg zeta function, Comm. Math. Phys. 110 (1987), 439-465.
• [17] W. I. Weisberger, Conformal invariants for determinants of Laplacians on Riemann surfaces, ibid. 112 (1987), 633-638.
• [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.