The large sieve, monodromy and zeta functions of curves
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.