The large sieve, monodromy and zeta functions of curves

2005/03/30 by Emmanuel Kowalski, Kowalski, Emmanuel · 1 citation
Mathematics · #11C08 #11G25 #11N35 #14D10 #14G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11C08 #msc:11G25 #msc:11N35 #msc:14D10 #msc:14G15

paper · pdf · doi:10.48550/arxiv.math/0503714

30 pages

arxiv created 2005/03/30 · arxiv updated 2009/12/01

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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• Mod-ℓ monodromy of double covers of ℙⁿ branched along hyperplane arrangements

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