Article ID Journal Published Year Pages File Type
8896975 Journal of Number Theory 2018 20 Pages PDF
Abstract
Let P:⋯→C2→C1→P1 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
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