Angles in hyperbolic lattices: The pair correlation density
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Angles in hyperbolic lattices : The pair correlation density. / Risager, Morten S.; Södergren, Carl Anders.
I: Transactions of the American Mathematical Society, Bind 369, Nr. 4, 2017, s. 2807-2841 .Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 369
SP - 2807
EP - 2841
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 4
ER -
ID: 126343978