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Abstract We compute moments of L-functions associated to the polynomial family of Artin–Schreier covers over $$\mathbb{F}_q$$, where q is a power of a prime p > 2, when the size of the finite field is fixed and the genus of the family goes to infinity. More specifically, we compute the $$k{\text{th}}$$ moment for a large range of values of k, depending on the sizes of p and q. We also compute the second moment in absolute value of the polynomial family, obtaining an exact formula with a lower order term, and confirming the unitary symmetry type of the family.
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Abelian Covers of ℙ1 of p -Ordinary Ekedahl–Oort Type
Abstract Given a family of abelian covers of $${\mathbb{P}}^{1}$$ and a prime $$p$$ of good reduction, by considering the associated Deligne–Mostow Shimura variety, we obtain non-trivial bounds for the Ekedahl–Oort types, and the Newton polygons, at prime $$p$$ for the curves in the family. In this paper, we investigate whether such bounds are sharp. In particular, we prove sharpness when the number of branching points is at most five and $$p$$ sufficiently large. Our result is a generalization under stricter assumptions of [ 2, Theorem 6.1] by Bouw, which proves the analogous statement for the $$p$$-rank, and it relies on the notion of Hasse–Witt triple introduced by Moonen in [ 12].
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- Award ID(s):
- 2200694
- PAR ID:
- 10552974
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2024
- Issue:
- 23
- ISSN:
- 1073-7928
- Format(s):
- Medium: X Size: p. 14369-14392
- Size(s):
- p. 14369-14392
- Sponsoring Org:
- National Science Foundation
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