The Large Sieve, Monodromy and Zeta Functions of Curves
نویسنده
چکیده
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.
منابع مشابه
The Large Sieve, Monodromy and Zeta Functions of Algebraic Curves, Ii: Independence of the Zeros
Using the sieve for Frobenius developed earlier by the author, we show that in a certain sense, the roots of the L-functions of most algebraic curves over finite fields do not satisfy any non-trivial (linear or multiplicative) dependency relations. This can be seen as an analogue of conjectures of Q-linear independence among ordinates of zeros of Lfunctions over number fields. As a corollary of...
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