Statistics for traces of cyclic trigonal curves over finite fields

Details Statistics for traces of cyclic trigonal curves over finite fields Statistics for traces of cyclic trigonal curves over finite fields

2009-07-30

arxiv.org/abs/0907.5434v2

Int. Math. Res. Not. IMRN 2010, no. 5, 932--967

Mathematics

Number Theory

30 pages, added statement and sketch of proof in Section 7 for generalization of results to p-fold covers of the projective li

Scientific paper

10.1093/imrn/rnp162

We study the variation of the trace of the Frobenius endomorphism associated to a cyclic trigonal curve of genus g over a field of q elements as the curve varies in an irreducible component of the moduli space. We show that for q fixed and g increasing, the limiting distribution of the trace of the Frobenius equals the sum of q+1 independent random variables taking the value 0 with probability 2/(q+2) and 1, e^{(2pi i)/3}, e^{(4pi i)/3} each with probability q/(3(q+2)). This extends the work of Kurlberg and Rudnick who considered the same limit for hyperelliptic curves. We also show that when both g and q go to infinity, the normalized trace has a standard complex Gaussian distribution and how to generalize these results to p-fold covers of the projective line.

Affiliated with

Also associated with

No associations

Rating

Statistics for traces of cyclic trigonal curves over finite fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Statistics for traces of cyclic trigonal curves over finite fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistics for traces of cyclic trigonal curves over finite fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-266998