A lattice point problem on the regular tree

作者：Douma Femke^*

来源：Discrete Mathematics, 2011, 311(4): 276-281.

DOI：10.1016/j.disc.2010.10.019

• Regular tree
• Lattice point counting
• Conjugacy class
• Eigenfunction

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 is an element of 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.

• 出版日期2011-2-28