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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

Prime geodesic theorem for the modular surface

Muharem Avdispahić(University of Sarajevo)0000-0001-7836-4988
Sayfa
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Yayın Tarihi
2020-04-02
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Under the generalized Lindelöf hypothesis, the exponent in the error term of the prime geodesic theorem for the modular surface is reduced to $\frac{5}{8}+\varepsilon$ outside a set of finite logarithmic measure.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Under the generalized Lindelöf hypothesis, the exponent in the error term of the prime geodesic theorem for the modular surface is reduced to $\frac{5}{8}+\varepsilon$ outside a set of finite logarithmic measure.
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Temel Bulgular & Veri:Under the generalized Lindelöf hypothesis, the exponent in the error term of the prime geodesic theorem for the modular surface is reduced to $\frac{5}{8}+\varepsilon$ outside a set of finite logarithmic measure.
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Sonuç & Katkı:Under the generalized Lindelöf hypothesis, the exponent in the error term of the prime geodesic theorem for the modular surface is reduced to $\frac{5}{8}+\varepsilon$ outside a set of finite logarithmic measure.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:prime geodesic theorem · Selberg zeta function · modular group

Abstract

Under the generalized Lindelöf hypothesis, the exponent in the error term of the prime geodesic theorem for the modular surface is reduced to $\frac{5}{8}+\varepsilon$ outside a set of finite logarithmic measure.

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Bu Makaleye Atıf Yap

Avdispahić, M. (2020). Prime geodesic theorem for the modular surface. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.568323

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Kaynakça (19)

  1. M. Avdispahić, Prime geodesic theorem of Gallagher type, arXiv:1701.02115, 2017.
  2. M. Avdispahić, On Koyama’s refinement of the prime geodesic theorem, Proc. Japan Acad. Ser. A Math. Sci. 94 (3), 21–24, 2018.
  3. M. Avdispahić, Gallagherian $PGT$ on $PSL(2,Z)$, Funct. Approx. Comment. Math. 58 (2), 207–213, 2018.
  4. M. Avdispahić, Errata and addendum to "On the prime geodesic theorem for hyperbolic 3-manifolds" Math. Nachr. 291 (2018), no. 14-15, 2160–2167, Math. Nachr. 292 (4), 691–693, 2019.
  5. O. Balkanova and D. Frolenkov, Bounds for a spectral exponential sum, J. London Math. Soc. 99 (2), 249–272, 2019.
  6. R. Blumenhagen and E. Plauschinn, Introduction to conformal field theory: With applications to string theory, in: Lect. Notes Phys. 779, Springer, Berlin Heidelberg, 2009.
  7. P. Buser, Geometry and spectra of compact Riemann surfaces, Progress in Mathe- matics 106, Birkhäuser, Boston-Basel-Berlin, 1992.
  8. Y. Cai, Prime geodesic theorem, J. Théor. Nombres Bordeaux, 14 (1), 59–72, 2002.
  9. J.B. Conrey and H. Iwaniec, The cubic moment of central values of automorphic L-functions, Ann. of Math. (2) 151 (3), 1175–1216, 2000.
  10. P.X. Gallagher, A large sieve density estimate near $\sigma =1$, Invent. Math. 11, 329–339, 1970.
  11. P.X. Gallagher, Some consequences of the Riemann hypothesis, Acta Arith. 37, 339– 343, 1980.
  12. D.A. Hejhal, The Selberg trace formula for PSL(2,R). Vol I, Lecture Notes in Math- ematics 548, Springer, Berlin, 1976.
  13. A.E. Ingham, The distribution of prime numbers, Cambridge University Press, 1932.
  14. H. Iwaniec, Non-holomorphic modular forms and their applications, in: Modular forms (Durham, 1983), Ellis Horwood Ser. Math. Appl.: Statist. Oper. Res., 157– 196, Horwood, Chichester, 1984.
  15. H. Iwaniec, Prime geodesic theorem, J. Reine Angew. Math. 349, 136–159, 1984.
  16. S. Koyama, Refinement of prime geodesic theorem, Proc. Japan Acad. Ser A Math. Sci. 92 (7), 77–81, 2016.
  17. W. Luo and P. Sarnak, Quantum ergodicity of eigenfunctions on $PSL_{2}(Z)\backslash H^{2}$, Inst. Hautes Études Sci. Publ. Math. 81, 207–237, 1995.
  18. B. Randol, On the asymptotic distribution of closed geodesics on compact Riemann surfaces, Trans. Amer. Math. Soc. 233, 241–247, 1977.
  19. K. Soundararajan and M.P. Young, The prime geodesic theorem, J. Reine Angew. Math. 676, 105–120, 2013.