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- W1900381090 abstract "Let $Gamma$ be a cocompact discrete subgroup of $mathrm{PSL}_{2}(mathbb{C})$ and denote by $mathcal{H}$ the three dimensional upper half-space. For a $pinmathcal{H}$, we count the number of points in the orbit $Gamma p$, according to their distance, $operatorname{arccosh} X$, from a totally geodesic hyperplane. The main term in $n$ dimensions was obtained by Herrmann for any subset of a totally geodesic submanifold. We prove a pointwise error term of $O(X^{3/2})$ by extending the method of Huber and Chatzakos-Petridis to three dimensions. By applying Chamizo's large sieve inequalities we obtain the conjectured error term $O(X^{1+epsilon})$ on average in the spatial aspect. We prove a corresponding large sieve inequality for the radial average and explain why it only improves on the pointwise bound by $1/6$." @default.
- W1900381090 created "2016-06-24" @default.
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- W1900381090 date "2017-02-27" @default.
- W1900381090 modified "2023-10-16" @default.
- W1900381090 title "Lattice point counting in sectors of Hyperbolic 3-space" @default.
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- W1900381090 doi "https://doi.org/10.1093/qmath/hax004" @default.
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