Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 2, 505 - 509, 02.04.2020
https://doi.org/10.15672/hujms.568323

Öz

Kaynakça

  • [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.

Prime geodesic theorem for the modular surface

Yıl 2020, Cilt: 49 Sayı: 2, 505 - 509, 02.04.2020
https://doi.org/10.15672/hujms.568323

Öz

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.

Kaynakça

  • [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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Muharem Avdispahić Bu kişi benim 0000-0001-7836-4988

Yayımlanma Tarihi 2 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 2

Kaynak Göster

APA Avdispahić, M. (2020). Prime geodesic theorem for the modular surface. Hacettepe Journal of Mathematics and Statistics, 49(2), 505-509. https://doi.org/10.15672/hujms.568323
AMA Avdispahić M. Prime geodesic theorem for the modular surface. Hacettepe Journal of Mathematics and Statistics. Nisan 2020;49(2):505-509. doi:10.15672/hujms.568323
Chicago Avdispahić, Muharem. “Prime Geodesic Theorem for the Modular Surface”. Hacettepe Journal of Mathematics and Statistics 49, sy. 2 (Nisan 2020): 505-9. https://doi.org/10.15672/hujms.568323.
EndNote Avdispahić M (01 Nisan 2020) Prime geodesic theorem for the modular surface. Hacettepe Journal of Mathematics and Statistics 49 2 505–509.
IEEE M. Avdispahić, “Prime geodesic theorem for the modular surface”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 2, ss. 505–509, 2020, doi: 10.15672/hujms.568323.
ISNAD Avdispahić, Muharem. “Prime Geodesic Theorem for the Modular Surface”. Hacettepe Journal of Mathematics and Statistics 49/2 (Nisan 2020), 505-509. https://doi.org/10.15672/hujms.568323.
JAMA Avdispahić M. Prime geodesic theorem for the modular surface. Hacettepe Journal of Mathematics and Statistics. 2020;49:505–509.
MLA Avdispahić, Muharem. “Prime Geodesic Theorem for the Modular Surface”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 2, 2020, ss. 505-9, doi:10.15672/hujms.568323.
Vancouver Avdispahić M. Prime geodesic theorem for the modular surface. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):505-9.

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