Author:
BUCUR ALINA,COSTA EDGAR,DAVID CHANTAL,GUERREIRO JOÃO,LOWRY–DUDA DAVID
Abstract
AbstractThe zeta function of a curve C over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix ΘC. We develop and present a new technique to compute the expected value of tr(ΘCn) for various moduli spaces of curves of genus g over a fixed finite field in the limit as g is large, generalising and extending the work of Rudnick [Rud10] and Chinis [Chi16]. This is achieved by using function field zeta functions, explicit formulae, and the densities of prime polynomials with prescribed ramification types at certain places as given in [BDF+16] and [Zha]. We extend [BDF+16] by describing explicit dependence on the place and give an explicit proof of the Lindelöf bound for function field Dirichlet L-functions L(1/2 + it, χ). As applications, we compute the one-level density for hyperelliptic curves, cyclic ℓ-covers, and cubic non-Galois covers.
Publisher
Cambridge University Press (CUP)
Reference21 articles.
1. D. Fiorilli , J. Parks and A. Södergren Low-lying zeros of quadratic Dirichlet L-functions: Lower order terms for extended support. Preprint (2016), arXiv:1601.06833.
2. Density of discriminants of cubic extensions;Datskovsky;J. Reine Angew. Math.,1988
3. Some extremal functions in Fourier analysis. II
4. Bounding |ζ(½+it
)| on the Riemann hypothesis
5. Traces of high powers of the Frobenius class in the moduli space of hyperelliptic curves
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