Sieve in discrete groups, especially sparse

Abstract

We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.

26 pages; v2: add reference to earlier Erdos-Kac-type theorem of Djankovic for Apollonian curvatures

References in corpus (8)

• Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces
• Random walks on the mapping class group
• The ergodic theory of lattice subgroups
• Exponential decay in the mapping class group
• Expansion in $S{L}_d(O_K/I)$, $I$ square-free
• Splitting fields of characteristic polynomials of random elements in arithmetic groups
• On a variant of the large sieve
• Walks on graphs and lattices -- effective bounds and applications

Cited by in corpus (1)

• Harmonic analysis, Ergodic theory and Counting for thin groups