Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897039 | Journal of Number Theory | 2018 | 16 Pages |
Abstract
Any polynomial f(x)âZq[x] defines a Witt vector [f]âW(Fq[x]). Consider the Artin-Schreier-Witt tower yFây=[f]. This is a tower of curves over Fq, with total Galois group Zp. We want to study the Newton slopes of zeta functions of this tower. We reduce it to the Newton polygons of L-functions associated with characters on the Galois groups. We prove that, when the conductors are large enough, these Newton slopes are unions of arithmetic progressions which are changing proportionally as the conductor increases. This is a generalization of the result of [1], where they get the same result in the case the non-zero coefficients of f(x) are roots of unity. To overcome the new difficulty in our process, we apply some (pθ,T)-topology.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Li Xiang,