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E Kowalski

The large sieve, monodromy and zeta functions of curves

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.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 12/2006
Pages: 29 - 69

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