A lattice point problem on the regular tree |
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Authors: | Femke Douma |
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Affiliation: | aDepartment of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, UK |
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Abstract: | Huber (1956) [8] considered the following problem on the hyperbolic plane H. Consider a strictly hyperbolic subgroup of automorphisms on H with compact quotient, and choose a conjugacy class in this group. Count the number of vertices inside an increasing ball, which are images of a fixed point x∈H under automorphisms in the chosen conjugacy class, and describe the asymptotic behaviour of this number as the size of the ball goes to infinity. We use a well-known analogy between the hyperbolic plane and the regular tree to solve this problem on the regular tree. |
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Keywords: | Regular tree Lattice point counting Conjugacy class Eigenfunction |
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