Prime geodesic theorem for the Picard manifold

Olga Balkanova; Dmitry Frolenkov

Prime geodesic theorem for the Picard manifold

Number Theory 2019-09-30 v3 Spectral Theory

Authors: Olga Balkanova , Dmitry Frolenkov

Abstract

Let $\Gamma=PSL(2,Z[i])$ be the Picard group and $H^3$ be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient $\Gamma \setminus H^3$ , called the Picard manifold, obtaining an error term of size $O(X^{3/2+\theta/2+\epsilon})$ , where $\theta$ denotes a subconvexity exponent for quadratic Dirichlet $L$ -functions defined over Gaussian integers.

Keywords

geodesics and riemannian geometry hyperbolic geometry lie groups

Cite

@article{arxiv.1804.00275,
  title  = {Prime geodesic theorem for the Picard manifold},
  author = {Olga Balkanova and Dmitry Frolenkov},
  journal= {arXiv preprint arXiv:1804.00275},
  year   = {2019}
}

Comments

Corrected subconvexity estimate in (3.24)

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