81 citations · 174 across the 25 of their papers we have counts for
13 papers · 1 filter
Automorphic density estimates and optimal Diophantine exponents
Mikolaj Fraczyk, Alexander Gorodnik, Amos Nevo
The present paper is devoted to establishing an optimal approximation exponent for the action of an irreducible uniform lattice subgroup of a product group on its proper factors. P…
On discrepancy, intrinsic Diophantine approximation, and spectral gaps
Alexander Gorodnik, Amos Nevo
In the present paper we establish bounds for the size of the spectral gap for actions of algebraic groups on certain homogeneous spaces. Our approach is based on estimating operato…
Discrepancy of rational points in simple algebraic groups
Alexander Gorodnik, Amos Nevo
The present paper analyzes the discrepancy of distribution of rational points on general semisimple algebraic group varieties. The results include mean-square, almost sure, and uni…
Counting intrinsic Diophantine approximations in simple algebraic groups
Anish Ghosh, Alex Gorodnik, Amos Nevo
We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple algebraic groups, at arbitrarily s…
Optimal density for values of generic polynomial maps
Anish Ghosh, Alexander Gorodnik, Amos Nevo
We establish that the optimal bound for the size of the smallest integral solution of the Oppenheim Diophantine approximation problem $\abs{Q(x)-ξ}< ε$ for a generic ternary form $…
Prime Points in Orbits: Some Instances of the Bourgain-Gamburd-Sarnak Conjecture
Tal Horesh, Amos Nevo
We use Vaughan's variation on Vinogradov's three-primes theorem to prove Zariski-density of prime points in several infinite families of hypersurfaces, including level sets of some…