Prime geodesic theorem

Yingchun Cai

doi:10.5802/jtnb.346

Yingchun Cai

Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 59-72

Abstract (VO)
Résumé

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

Soit $Γ = P S L (2, Z)$ . On démontre que $π_{Γ} (x) = li x + O (x^{\frac{71}{102} + ϵ}), ϵ > 0$ où l’exposant $\frac{71}{102}$ améliore l’exposant $\frac{7}{10}$ précédemment obtenu par W. Z. Luo et P. Sarnak.

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DOI : 10.5802/jtnb.346

Yingchun Cai. Prime geodesic theorem. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 59-72. doi: 10.5802/jtnb.346

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     title = {Prime geodesic theorem},
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     pages = {59--72},
     year = {2002},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
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     doi = {10.5802/jtnb.346},
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