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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

Prime geodesic theorem for the modular surface

Muharem Avdispahić
Sayfa
505–509
Yayın Tarihi
2022-10-18
DOI
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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:Araştırma Makalesi
📍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. (2022). Prime geodesic theorem for the modular surface. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 505–509. https://ajindex.com/articles/529679

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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.