journal article Sep 01, 1987

Spectral functions, special functions and the Selberg zeta function

View at Publisher Save 10.1007/bf01212422
Topics

No keywords indexed for this article. Browse by subject →

References
39
[1]
D'Hoker, E., Phong, D. H.: (a) Multiloop amplitudes for the bosonic Polyakov string. Nucl. Phys.B269, 205?234 (1986) 10.1016/0550-3213(86)90372-x
[2]
(b) On determinants of Laplacians on Riemann surfaces. Commun. Math. Phys.104, 537?545 (1986) 10.1007/bf01211063
[3]
Ray, D., Singer, I. M.: Ann. Math.98, 154?177 (1973) 10.2307/1970909
[4]
Donnelly, H.: Am. J. Math.101, 1365?1379 (1979) 10.2307/2374146
[5]
Fried, D.: Invent. Math.84, 523?540 (1986) 10.1007/bf01388745
[6]
Widder, D.: The Laplace Transform (Chap. V), Princeton. NJ: Princeton University Press 1946
[7]
Duistermaat, H., Guillemin, V. W.: Invent. Math.29, 39?79 (1975) 10.1007/bf01405172
[8]
Voros, A.: in: The Riemann problem.... Chudnovsky, D., Chudnovsky, G. (eds.) Lecture Notes in Mathematics Vol.925. Berlin, Heidelberg, New York: Springer 1982
[9]
Voros, A.: The return of the quartic oscillator. The complex WKB method. Ann. Inst. H. Poincaré39A, 211?338 (1983) (especially Sects. 4, 10 and Appendices A, C, D)
[10]
Hille, E.: Analytic function theory, Vol. I, Chap. 8.7 and Vol.II, Chap. 14, Blaisdell 1962?1963
[11]
Gelfand, I. M., Shilov, G. E.: Generalized functions Vol.1. New York: Academic Press 1964
[12]
Seeley, R.: AMS Proc. Symp. Pure Math.10, 288?307 (1966) 10.1090/pspum/010/0237943
[13]
Gelfand, I. M., Levitan, B. M.: Dokl. Akad. Nauk. SSSR88, 593?596 (1953), Dikii, L. A.: Usp. Math. Nauk13, 111?143 (1958) (Translations AMS Series 218, 81?115)
[14]
Barnes, E. W.: Q. J. Math.31, 264?314 (1900)
[15]
Whittaker, E. T., Watson, G. N.: A course of modern analysis, Cambridge: Cambridge University Press 1965
[16]
Erdelyi et al.: Higher transcendental functions Vol.1, Chap. 1 (Bateman Manuscript Project), New York: McGraw Hill 1953
[17]
Selberg, A.: J. Ind. Math. Soc.20, 47?87 (1956)
[18]
Hejhal, D. A.: Duke Math. J.43, 441?482 (1976) 10.1215/s0012-7094-76-04338-6
[19]
Balazs, N. L., Voros, A.: Chaos on the Pseudosphere. Phys. Rep.143, 109?240 (1986) 10.1016/0370-1573(86)90159-6
[20]
Huber, H.: Math. Anal.138, 1?26 (1959) 10.1007/bf01369663
[21]
Belavin, A., Knizhnik, V.: JETP91, 364?390 (1986); Manin, YU.: JETP Lett.43, 161?163 (1986)
[22]
Fried, D.: Invent. Math.84, 523?540 (1986) 10.1007/bf01388745
[23]
Kinkelin,: J. Reine Angew. Math. (Crelle)57, 122?138 (1860), Glaisher, J. W. L.: Messenger of Math.6, 71?76 (1877) and24, 1?16 (1894) 10.1515/crll.1860.57.122
[24]
Cartier, P.: Analyse numérique d'un problème de valeurs propres à haute précision (Application aux fonctions automorphes), IHES preprint (1978);
[25]
Vigneras, M-F.: Astérique61, 235?249 (1979)
[26]
The Strong Szego Limit Theorem for Circular Arcs

Harold Widom

Indiana University Mathematics Journal 1971 10.1512/iumj.1972.21.21022
[27]
Widom, H.: Am. J. Math.95, 333?383 (1973); McCoy, B., Wu, T. T.: The two-dimensional Ising model, Cambridge, MA; Harvard University Press 1973 (page 264 and Appendix B); Dyson, F. J.: Fredholm determinants and inverse scattering problems. Commun. Math. Phys.47, 171?183 (1976) 10.2307/2373789
[28]
Hardy, G. H.: Divergent Series, Clarendon Press, Oxford 1949
[29]
Gradshteyn, I. S., Ryzhik, I. M.: Tables of integrals, series and products (Corrected and Enlarged Edition prepared by A. Jeffrey), New York: Academic Press 1980
[30]
Lenard, A.: Pacific J. Math.42, 137?145 (1972) 10.2140/pjm.1972.42.137
[31]
Olver, F. W. J.: Asymptotics and special functions (Chap. 8, Sects. 2.2 and 3.3). New York: Academic Press 1974
[32]
Vardi, I.: Determinants of Laplacians and multiple gamma functions. Stanford Math. preprint (Sept. 1986), submitted to SIAM J. Math. Anal.; Weisberger, W. I.: Normalization of the path integral measure and the coupling constants for basonic strings, Nucl. Phys. B (in press) (1987)
[33]
Elstrodt, J.: Jber. d. Dt. Math. Verein83, 45?77 (1981), Eq. (10.5)
[34]
Randol, B.: Trans. AMS201, 241?246 (1975) 10.1090/s0002-9947-1975-0369286-6
[35]
Selberg, A.: Lectures 1953?1954 (unpublished; private communication of J. Elstrodt); Randol, B.: Trans. AMS233, 241?247 (1977); Elstrodt, J., Grunewald, F., Mennicke, J.: Elementary and analytic theory of numbers. Banach center publications17, 83?120 (1985) (Warsaw) 10.1090/s0002-9947-1977-0482582-9
[36]
Fischer, J.: Dissertation, Univ. Münster 1985 (and ?An Approach to the Selberg trace formula via the Selberg zeta function?, submitted to Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer)
[37]
Sarnak, P.: Determinants of Laplacians, Comm. Math. Phys. (in press) (1987) 10.1007/bf01209019
[38]
Balazs, N. L., Schmit, C., Voros, A.: Spectral fluctuations and zeta functions. Saclay preprint PhT/86-156. J. Stat. Phys. (to appear) (M. Kac memorial issue)
[39]
Voros, A.: Phys. Lett.B180, 245?246 (1986) 10.1016/0370-2693(86)90303-5
Metrics
290
Citations
39
References
Details
Published
Sep 01, 1987
Vol/Issue
110(3)
Pages
439-465
License
View
Authors
Cite This Article
A. Voros (1987). Spectral functions, special functions and the Selberg zeta function. Communications in Mathematical Physics, 110(3), 439-465. https://doi.org/10.1007/bf01212422
Related

You May Also Like

Particle creation by black holes

S. W. Hawking · 1975

10,628 citations

On the generators of quantum dynamical semigroups

G. Lindblad · 1976

6,183 citations

The four laws of black hole mechanics

J. M. Bardeen, B. Carter · 1973

3,127 citations

Non-abelian bosonization in two dimensions

Edward Witten · 1984

1,940 citations

Intermittent transition to turbulence in dissipative dynamical systems

Yves Pomeau, PAUL MANNEVILLE · 1980

1,701 citations