Gallagherian Prime Geodesic Theorem in Higher Dimensions

Abstract

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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Acknowledgements

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). https://doi.org/10.1007/s40840-019-00849-y

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Keywords

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

Mathematics Subject Classification

  • 11M36
  • 11F72
  • 58J50