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Alina Bucur : Traces of high powers of Frobenius for cubic covers of the projective line over finite fields

The zeta function of a curve C over a finite field can be expressed in terms of the characteristic polynomial of its Frobenius endomorphism. We will see how one can compute the trace of high powers of this endomorphism in various moduli spaces. Finally, we will discuss how one can use this information to compute the one-level density -- which concerns low-lying zeros of the zeta function -- in the case of cubic covers of the projective line.

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