The Large Sieve and Galois Representations

Details The Large Sieve and Galois Representations The Large Sieve and Galois Representations

2008-12-11

arxiv.org/abs/0812.2222v1

Mathematics

Number Theory

36 pages

Scientific paper

We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system of representations arising from the Galois action on the torsion points of an abelian variety. The resulting upper bounds require explicit character sum calculations, with stronger results holding if one assumes the Generalized Riemann Hypothesis.

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