Dzenan Gusic, "On Asymptotic Behavior of Zeta Singularities for Compact Locally Symmetric Spaces," WSEAS Transactions on Mathematics, vol. 19, pp. 463-474, 2020, DOI:10.37394/23206.2020.19.49
Dzenan Gusic. On Asymptotic Behavior of Zeta Singularities for Compact Locally Symmetric Spaces.
WSEAS Transactions on Mathematics. 2020;19:463-474. 10.37394/23206.2020.19.49
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 19, 2020
On Asymptotic Behavior of Zeta Singularities for Compact Locally Symmetric Spaces
Author:
Abstract: We obtain precise estimates for the number of singularities of Selberg’s and Ruelle’s zeta functions for compact, higher-dimensional, locally symmetric Riemannian manifolds of strictly negative sectional curvature. The methods applied in this research represent a generalization of the methods described in the case of a compact Riemann surface. In particular, this includes an application of the Phragmen-Lindelof theorem, the variation of the argument of certain zeta functions, as well as the use of some classical analytic number theory techniques.
Keywords:
Phragmen-Lindelof theorem, zeta functions, distrubution of singularities, compact locally symmetric spaces, counting functions
Pages: 463-474 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 19, 2020, Art. #49 DOI: 10.37394/23206.2020.19.49
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