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Dzenan Gusic



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Dzenan Gusic


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 17, 2018



Prime Geodesic Theorem for Compact Even-Dimensional Locally Symmetric Riemannian Manifolds of Strictly Negative Sectional Curvature

AUTHORS: Dzenan Gusic

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ABSTRACT: Applying a suitably derived, Titchmarsh-Landau style approximate formula for the logarithmic derivative of the Ruelle zeta function, we obtain an another proof of the recently improved variant of the prime geodesic theorem for compact, even-dimensional, locally symmetric spaces of real rank one

KEYWORDS: Prime geodesic theorem, Selberg zeta function, Ruelle zeta function

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[3] M. Avdispahic and D ´ z. Gu ˇ siˇ c, On the length ´ spectrum for compact locally symmetric spaces of real rank one, WSEAS Trans. on Math. 16, 2017, pp. 303-321.

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[10] Y. Gon and J. Park, The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps, Math. Ann. 346, 2010, pp. 719–767.

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[17] S. Lang, Algebraic Number Theory, Adison– Wesley, Mass. 1968

[18] W. Luo and P. Sarnak, Quantum ergodicity of eigenfunctions on PSL2 (R) \ H2 , Inst. Hautes E´tudes Sci. Publ. Math. 81, 1995, pp. 207–237.

[19] J. Park, Ruelle zeta function and prime geodesic theorem for hyperbolic manifolds with cusps, in: G. van Dijk, M. Wakayama (eds.), Casimir force, Casimir operators and Riemann hypothesis, de Gruyter, Berlin 2010, pp. 89–104.

[20] M. Pavey, Class Numbers of Orders in Quartic Fields, Ph.D. dissertation, University of T¨ubingen, 2006.

[21] B. Randol, On the asymptotic distribution of closed geodesics on compact Riemann surfaces, Trans. Amer. Math. Soc. 233, 1977, pp. 241–247.

[22] D. Ruelle, Dynamical zeta functions and transfer operators, Notices Amer. Math. Soc. 49, 2002, pp. 887–895.

[23] K. Soundararajan and M.–P. Young, The prime geodesic theorem, J. Reine Angew. Math. 676, 2013, pp. 105–120.

[24] E.–C. Titchmarsh, The Theory of the Riemann Zeta-function, Claredon–Press, Oxford 1986

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #24, pp. 188-196


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