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Muharem Avdispahić
Dženan Gušić



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Muharem Avdispahić
Dženan Gušić


WSEAS Transactions on Mathematics


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

Volume 16, 2017

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 16, 2017



On the Length Spectrum for Compact Locally Symmetric Spaces of Real Rank One

AUTHORS: Muharem Avdispahić, Dženan Gušić

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ABSTRACT: We obtain improved asymptotic estimate for the function enumerating prime geodesics over compact locally symmetric space of real rank one.

KEYWORDS: length spectrum, zeta functions, logarithmic derivative, entire and meromorphic functions, functional equations, admissible lifts

REFERENCES:

[1] M. Avdispahic and Dz. Gusic, On the error term in the prime geodesic theorem, Bull. Korean Math. Soc., Vol.49, 2012, pp. 367-372.

[2] M. Avdispahic and Dz. Gusic, Order of Selberg’s and Ruelle’s zeta functions for compact even-dimensional locally symmetric spaces, J. Math. Anal. Appl., Vol.413, 2014, pp. 525-531.

[3] M. Avdispahic, Dz. Gusic and D. Kamber, Order of zeta functions for compact evendimensional symmetric spaces, Bull. Hellenic Math., Vol.59, 2016, pp. 57-69.

[4] M. Avdispahic and L. Smajlovic, On the prime number theorem for a compact Riemann surface, Rocky Mountain J. Math., Vol.39, 2009, pp. 1837-1845.

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[18] D. Hejhal, The Selberg trace formula for PSL(2,R). Vol. II. Lecture Notes in Mathematics 1001, Springer-Verlag, 1983.

[19] A. E. Ingham, The distribution of prime numbers, Cambridge Univ. Press, 1990.

[20] J. Park, Ruelle zeta function and prime geodesic theorem for hyperbolic manifolds with cusps, in: Casimir force, Casimir Operators and Riemann hypothesis, Berlin 2010, pp. 89-104.

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

[22] B. Randol, The Riemann hypothesis for Selberg’s zeta-function and the asymptotic behavior of eigenvalues of the Laplace operator, Trans. Amer. Math. Soc., Vol.236, 1978, pp. 209-223.

[23] M. Wakayama, Zeta functions of Selberg’s type associated with homogeneous vector bundles, Hiroshima Math. J., Vol.15, 1985, pp. 235-295

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #35, pp. 303-321


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