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arXiv · 1804.00275

Prime geodesic theorem for the Picard manifold

Olga Balkanova·Dmitry Frolenkov
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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.

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Olga Balkanova, Dmitry Frolenkov. 2018-04-01. Prime geodesic theorem for the Picard manifold. https://arxiv.org/abs/1804.00275

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