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.
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Communicated by Rosihan M. Ali.
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Avdispahić, M. On von Koch Theorem for PSL(2,\(\mathbb {Z}\)). Bull. Malays. Math. Sci. Soc. 44, 2139–2150 (2021). https://doi.org/10.1007/s40840-020-01053-z
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DOI: https://doi.org/10.1007/s40840-020-01053-z