… respect to subgroups of SL,(Z), modular symbols have served … = SL3/Q and a torsion-free
subgroup r of finite index in SL, (Z)… P of SL3 (R) one has the associated modular symbol (cf. 92), …

… We show a prime geodesic theorem for the group SL 3 ⁢ ( ℤ ) counting those geodesics
whose lifts lie in the split Cartan subgroup. This is the first arithmetic prime geodesic …

… We denote by F = Z&(Z) the group of 3 x 3 integral matrices with determinant … The end
of this paragraph is devoted to the proof of the theorem. We shall make use of the “geodesic …

… , we adapt the algebraic proof that SL2(Z) = 〈S, T〉, except instead of the usual division
theorem in Z we will use the modified division theorem in Z: if a, b ∈ Z with b = 0 then a = bq + r …

… an SL3 Maass form to a maximal flat subspace. … Z/nH and ` is the infinite vertical geodesic
from i to i1, or a compact segment thereof, Ghosh, Reznikov, and Sarnak [18, Theorems …

… So if we identify IV(r,,(Z, p)) with H,(r,,(2,p)) via Theorem 3.2 and transfer the action of s, we
see that sfx, y) = -f(-x, y). Hence the set off’s satisfying (i) and (ii) of Definition 3.13 are exactly …

… Theorems 2 and 3 and the groups constructed in [Bourgain and Kontorovich, 2010] should
exist for infinite index subgroups Λ of SL3(Z), and the main theorem … subgroups of SL3(Z). In …

… In this paper our calculation concerns SL∗(3, Z), so we can draw this edge as a hyperbolic
geodesic in the upper half-space H3 := {(x, y, z)|x, y, z ∈ R, z ≥ 0}. The orbit O(β, α) is also a …

… These coordinates are chosen, since we will use analogous ones for SL(3, Z). They have …
3, Z) which is as good as that for SL(2, Z). There are many applications of the study of SL(2, Z) \ …

… To prove Theorem 1, however, we will replace (ZjS) X (Z/8)* with the group SL(3,Z/2). For
reasons which we will explain below, SL(3,Z/2) should be close to optimal for this problem. …