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Jun 8, 2014 at 1:06 comment added Andreas Holmstrom Ah, I see. Thanks Antoine, and Felipe!
Jun 7, 2014 at 13:35 comment added ACL @AndreasHolmstrom: because the functional equation shows that the zeta function (a rational function) has less independent coefficients than what you would think, roughly half of it.
Jun 7, 2014 at 10:57 comment added Andreas Holmstrom Felipe, how does the functional equation help here?
Jun 7, 2014 at 2:18 comment added Felipe Voloch @AndreasHolmstrom This is a precise question. If you have the point counts up to extensions of degree $\sum b_i$, then you'd have all the eigenvalues of Frobenius and thus the local zeta function. One can do a little better using the functional equation.
Jun 6, 2014 at 22:12 comment added Andreas Holmstrom I guess part of what I ask is whether one in general can describe the coefficients in terms of point counts, and if so, how far up in the tower of fields above F_p would you have to perform such point counts in order to describe the coefficients?
Jun 6, 2014 at 21:56 comment added Andreas Holmstrom They numbers a_p are the same in the sense that they all are given by counting points in the fiber. They are also the same in the sense that they are all given as Frobenius traces of the same global object. Does that make the question more sensible?
Jun 6, 2014 at 21:50 history answered ACL CC BY-SA 3.0