Gallagherian Prime Geodesic Theorem in Higher Dimensions


Using the Gallagher–Koyama approach, we reduce the exponent in the error term of the prime geodesic theorem for real hyperbolic manifolds with cusps.

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We would like to thank the referee for suggestions that resulted in adding the remark on lower dimensions (and related references) to the initial version of the paper.

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Correspondence to Zenan Šabanac.

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Communicated by Emrah Kilic.

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Avdispahić, M., Šabanac, Z. Gallagherian Prime Geodesic Theorem in Higher Dimensions. Bull. Malays. Math. Sci. Soc. 43, 3019–3026 (2020).

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  • Hyperbolic manifolds
  • Prime geodesic theorem
  • Selberg and Ruelle zeta functions

Mathematics Subject Classification

  • 11M36
  • 11F72
  • 58J50