Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896975 | Journal of Number Theory | 2018 | 20 Pages |
Abstract
Let P:â¯âC2âC1âP1 be a Zp-cover of the projective line over a finite field of cardinality q and characteristic p which ramifies at exactly one rational point. We study the q-adic valuations of the reciprocal roots in Cp of L-functions associated to characters of the Galois group of P. We show that for all covers P such that the genus of Cn is a quadratic polynomial in pn for n large, the valuations of these reciprocal roots are uniformly distributed in the interval [0,1]. Furthermore, we show that for a large class of such covers P, the valuations of the reciprocal roots in fact form a finite union of arithmetic progressions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Michiel Kosters, Hui June Zhu,