Selberg Zeta Function
المؤلف:
Fried, D
المصدر:
"Analytic Torsion and Closed Geodesics on Hyperbolic Manifolds." Invent. Math. 84
الجزء والصفحة:
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25-7-2019
3051
Selberg Zeta Function
Let 
run over all distinct primitive ordered periodic geodesics, and let 
denote the positive length of 
, then the Selberg zeta function is defined as
![Z(s)=product_(<span style=]() {p})product_(k=0)^infty[1-e^(-tau(p)(s+k))], " src="http://mathworld.wolfram.com/images/equations/SelbergZetaFunction/NumberedEquation1.gif" style="height:45px; width:175px" /> |
for 
.
REFERENCES:
d'Hoker, E. and Phong, D. H. "Multiloop Amplitudes for the Bosonic Polyakov String." Nucl. Phys. B 269, 205-234, 1986.
d'Hoker, E. and Phong, D. H. "On Determinants of Laplacians on Riemann Surfaces." Commun. Math. Phys. 104, 537-545, 1986.
Fried, D. "Analytic Torsion and Closed Geodesics on Hyperbolic Manifolds." Invent. Math. 84, 523-540, 1986.
Selberg, A. "Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces with Applications to Dirichlet Series." J. Indian Math. Soc. 20, 47-87, 1956.
Voros, A. "Spectral Functions, Special Functions and the Selberg Zeta Function." Commun. Math. Phys. 110, 439-465, 1987.
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