On the prime geodesic theorem for hyperbolic 3-manifolds

Muharem Avdispahić

doi:10.1002/mana201700190

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arXiv · 1705.05626

On the prime geodesic theorem for hyperbolic 3-manifolds

Muharem Avdispahić

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Abstract

Through the Selberg zeta approach, we reduce the exponent in the error term of the prime geodesic theorem for cocompact Kleinian groups or Bianchi groups from Sarnak's $\frac{5}{3}$ to $\frac{3}{2}$. At the cost of excluding a set of finite logarithmic measure, the bound is further improved to $\frac{13}{9}$.

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Muharem Avdispahić. 2017-05-16. On the prime geodesic theorem for hyperbolic 3-manifolds. https://doi.org/10.1002/mana201700190

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