Alexander Lubotzky

most citedDivision Algebras and Non-Commensurable Isospectral Manifolds

12 citations · 16 across the 6 of their papers we have counts for

collaborators

6 papers

math.CO2005

Isospectral Cayley graphs of some finite simple groups

Alexander Lubotzky, Beth Samuels, Uzi Vishne

We apply spectral analysis of quotients of the Bruhat-Tits buildings of type $A ~_{d - 1}$ to construct isospectral non-isomorphic Cayley graphs of the finite simple groups $\o…

math.SP2005★ 12 cited

Division Algebras and Non-Commensurable Isospectral Manifolds

Alexander Lubotzky, Beth Samuels, Uzi Vishne

A. Reid showed that if $Γ_{1}$ and $Γ_{2}$ are arithmetic lattices in $G = PGL_{2} (R)$ or in $PGL_{2} (C)$ which give rise to isospectral manif…

math.GR2004

Counting congruence subroups

D. Goldfeld, A. Lubotzky, L. Pyber

Let $Γ$ denote the modular group $S L (2, Z)$ and $C_{n} (Γ)$ the number of congruence subgroups of $Γ$ of index at most $n$ . We prove that $\lim\limits_{n\to \infty} \frac{\log C_n…

math.GR2004

Subgroup growth of lattices in semisimple Lie groups

A. Lubotzky, N. Nikolov

We give very precise bounds for the congruence subgroup growth of arithmetic groups. This allows us to determine the subgroup growth of irreducible lattices of semisimple Lie group…

math.CO2004★ 3 cited

Explicit Constructions of Ramanujan Complexes of Type $A ~_{d}$

Alex Lubotzky, Beth Samuels, Uzi Vishne

In this paper we present for every $d \geq 2$ and every local field $F$ of positive characteristic, explicit constructions of Ramanujan complexes which are quotients of the Bruhat-…

math.RT2004★ 1 cited

Ramanujan Complexes of Type $A_{d} ~$