The large sieve, monodromy and zeta functions of curves

Emmanuel Kowalski

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arXiv · math/0503714

The large sieve, monodromy and zeta functions of curves

Emmanuel Kowalski

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Abstract

We prove a large sieve statement for the average distribution of Frobenius conjugacy classes in arithmetic monodromy groups over finite fields. As a first application we prove a stronger version of a result of Chavdarov on the ``generic'' irreducibility of the numerator of the zeta functions in a family of curves with large monodromy.

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Emmanuel Kowalski. 2005-03-30. The large sieve, monodromy and zeta functions of curves. https://arxiv.org/abs/math/0503714

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