Prime geodesic theorem

Cai, Yingchun

Cai, Yingchun

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

Résumé
Abstract

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.

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.

MR Zbl

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     author = {Cai, Yingchun},
     title = {Prime geodesic theorem},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {59--72},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {1},
     year = {2002},
     mrnumber = {1925990},
     zbl = {1028.11030},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2002__14_1_59_0/}
}

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Cai, Yingchun. Prime geodesic theorem. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 59-72. http://www.numdam.org/item/JTNB_2002__14_1_59_0/

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