## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### On Koyama’s refinement of the prime geodesic theorem

Muharem Avdispahić

#### Abstract

We give a new proof of the best presently-known error term in the prime geodesic theorem for compact hyperbolic surfaces, without the assumption of excluding a set of finite logarithmic measure. Stronger implications of the Gallagher-Koyama approach are derived, yielding to a further reduction of the error term outside a set of finite logarithmic measure.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 94, Number 3 (2018), 21-24.

Dates
First available in Project Euclid: 28 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1519808413

Digital Object Identifier
doi:10.3792/pjaa.94.21

#### Citation

Avdispahić, Muharem. On Koyama’s refinement of the prime geodesic theorem. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 3, 21--24. doi:10.3792/pjaa.94.21. https://projecteuclid.org/euclid.pja/1519808413

#### References

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