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Prime geodesic theorem

Yingchun Cai — 2002

Journal de théorie des nombres de Bordeaux

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.

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