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.
"On Koyama’s refinement of the prime geodesic theorem." Proc. Japan Acad. Ser. A Math. Sci. 94 (3) 21 - 24, March 2018. https://doi.org/10.3792/pjaa.94.21