On von Koch Theorem for PSL(2,$$\mathbb {Z}$$)

Abstract

Under a previously studied condition on the argument of the Selberg zeta function on the critical line, we reach the critical exponent $$\frac{1}{2}$$ in the error term of the prime geodesic theorem for the modular group PSL(2, $$ \mathbb {Z}$$ ) outside a set of finite logarithmic measure. We also prove a conditional prime geodesic theorem of Hejhal’s type in this setting without the latter exclusion.