Angles in hyperbolic lattices: The pair correlation density

TY - JOUR

T1 - Angles in hyperbolic lattices

T2 - The pair correlation density

AU - Risager, Morten S.

AU - Södergren, Carl Anders

PY - 2017

Y1 - 2017

N2 - It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the density function in both the small and large variable limits. This extends earlier results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in dimension 2 to general dimension n . Our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead to effective results with explicit rates.

AB - It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the density function in both the small and large variable limits. This extends earlier results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in dimension 2 to general dimension n . Our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead to effective results with explicit rates.

U2 - 10.1090/tran/6770

DO - 10.1090/tran/6770

M3 - Journal article

SN - 0002-9947

VL - 369

SP - 2807

EP - 2841

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 4

ER -