The large sieve and random walks on left cosets of arithmetic groups

Florent Jouve (1)

1 IMB - Institut de Mathématiques de Bordeaux

Applying E. Kowalski's recent generalization of the large sieve we prove that certain properties expected to be typical (irreducibility of the characteristic polynomial, absence of squares among the matrix coefficients...) are indeed verified by most (in a very explicit sense) of the elements of GL(n,A) with fixed determinant (where A is an intermediate ring between Z and Q that we specify) or by (special) orthogonal matrices with integral entries and fixed spinor norm.

Domaines: Théorie des nombres [math.NT]

Florent Jouve. The large sieve and random walks on left cosets of arithmetic groups. 2008. ⟨hal-00387280⟩