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

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

2008-11-11

arxiv.org/abs/0811.1793v1

Mathematics

Number Theory

39 pages

Scientific paper

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.

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