Prime geodesic theorem

Yingchun Cai

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 1, page 59-72
  • ISSN: 1246-7405

Abstract

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Let Γ denote the modular group P S L ( 2 , Z ) . In this paper it is proved that π Γ ( x ) = li x + O ( x 71 102 + ϵ ) , ϵ > 0 . The exponent 71 102 improves the exponent 7 10 obtained by W. Z. Luo and P. Sarnak.

How to cite

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Cai, Yingchun. "Prime geodesic theorem." Journal de théorie des nombres de Bordeaux 14.1 (2002): 59-72. <http://eudml.org/doc/248896>.

@article{Cai2002,
abstract = {Let $\Gamma $ denote the modular group $PSL(2, Z)$. In this paper it is proved that $\pi _\Gamma (x) = \text\{li\} x + O(x^\{\frac\{71\}\{102\} + \epsilon \}), \epsilon &gt; 0$. The exponent $\frac\{71\}\{102\}$ improves the exponent $\frac\{7\}\{10\}$ obtained by W. Z. Luo and P. Sarnak.},
author = {Cai, Yingchun},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {prime geodesic theorem; modular group},
language = {eng},
number = {1},
pages = {59-72},
publisher = {Université Bordeaux I},
title = {Prime geodesic theorem},
url = {http://eudml.org/doc/248896},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Cai, Yingchun
TI - Prime geodesic theorem
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 1
SP - 59
EP - 72
AB - Let $\Gamma $ denote the modular group $PSL(2, Z)$. In this paper it is proved that $\pi _\Gamma (x) = \text{li} x + O(x^{\frac{71}{102} + \epsilon }), \epsilon &gt; 0$. The exponent $\frac{71}{102}$ improves the exponent $\frac{7}{10}$ obtained by W. Z. Luo and P. Sarnak.
LA - eng
KW - prime geodesic theorem; modular group
UR - http://eudml.org/doc/248896
ER -

References

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  9. [9] Z. Luo, P. Sarnak, Quantum ergodicity of eigenfunctions on PSL2(Z). Inst. Hautes. Etudes Sci. Publ. Math.81 (1995), 207-237. Zbl0852.11024
  10. [10] Z. Luo, Z. Rudnick, P. Sarnak, On Selberg's eigenvalue Conjecture. Geom. Funct. Anal.5 (1995), 387-401. Zbl0844.11038MR1334872
  11. [11] R.A. Rankin, Contribution to the theory of Ramanujan's function τ(n) and similar arithmetical functions. Proc. Cambridge. Phil. Soc.35 (1939), 351—372. Zbl0021.39201
  12. [12] P. Sarnak, Class number of infinitely binary quadratic forms. J. Number Theory15 (1982), 229-247. Zbl0499.10021MR675187
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