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- Title
The p-rank of the reduction p of Jacobians and Jacobi sums.
- Authors
Álvarez, A.
- Abstract
Let YK → XK be a ramified cyclic covering of curves, where K is a cyclotomic field. In this work we study the p-rank of the reduction p of a model of the Jacobian of YK. In this way, we obtain counterparts of the Deuring polynomial, defined for elliptic curves, for genus greater than one. We provide a new point of view of this subject in terms of L-functions. To carry out this study we use the relationship between Jacobi sums and L-functions. This is established in [A. Weil, Jacobi sums as "Grössencharaktere", Trans. Amer. Math. Soc. 73 (1952) 487-495] for the case of Fermat curves. We also give a new proof of a result of Deligne concerning the constant terms of these L-functions and Jacobi sums.
- Subjects
JACOBIAN matrices; JACOBI sums; CYCLOTOMIC fields; FIELD extensions (Mathematics); L-functions; POLYNOMIALS
- Publication
International Journal of Number Theory, 2014, Vol 10, Issue 8, p2097
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042114500705