Slopes of L-functions of Z_p-covers of the projective line

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Michiel Kosters
Tue, 02/21/2017 - 2:00pm - 3:00pm
RH 340P

Let P: ... -> C_2 -> C_1 -> P^1 be a Z_p-cover of the projective line over a finite field of characteristic p which ramifies at exactly one rational point. In this talk, we study the p-adic Newton slopes of L-functions associated to characters of the Galois group of P. It turns out that for covers P such that the genus of C_n is a quadratic polynomial in p^n for n large, the Newton slopes are uniformly distributed in the interval [0,1]. Furthermore, for a large class of such covers P, these slopes behave in an even more regular way. This is joint work with Hui June Zhu.