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On the growth of the number of primitive totally geodesic surfaces in some hyperbolic 3-manifolds

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Abstract Let d be a positive square-free integer ≡ 3 ( mod 4 ) such that the ideal class group of Q [ − d ] does not contain an… Click to show full abstract

Abstract Let d be a positive square-free integer ≡ 3 ( mod 4 ) such that the ideal class group of Q [ − d ] does not contain an element of order 4. We prove an asymptotic formula for the number of primitive immersed totally geodesic surfaces in Γ − d \ H 3 having area less than X.

Keywords: number; geodesic surfaces; growth number; number primitive; totally geodesic; primitive totally

Journal Title: Journal of Number Theory
Year Published: 2019

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