  Let L and L' be two integral Euclidean lattices in the same genus. We give an
asymptotic formula for the number of Kneser p-neighbors of L which are
isometric to L', when the prime p goes to infinity. In the case L is
unimodular, and if we fix furthermore a subgroup A of L, we also give an
asymptotic formula for the number of p-neighbors of L containing A and which
are isomorphic to L'. These statements explain numerical observations in the
recent classifications of unimodular lattices of rank 26, 27 and 28, by B.
Allombert and the author. The proofs use the existence of global Arthur
parameters associated to automorphic representations of definite orthogonal
groups over the rationals, which is deduced from Arthur's results in an
Appendix by O. Ta\"ibi.
