PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan.

Title:Statistics for the traces of cyclic p-covers of curves over finite fields
Seminar:Algebra and Number Theory Seminar
Speaker:Chantal David, IAS Princeton
Abstract:
We study in this talk the variation of the trace of the Frobenius endomorphism associated to curves C which have a cyclic p-fold cover over F_q as the curves vary in an irreducible component of the moduli space of cyclic p-covers of a fixed genus g. We show that for q fixed and g increasing, the limiting distribution of the trace of the Frobenius endomorphism is equal to the sum of q+1 independent random variables taking the value 0 with probability (p-1)/(q+p-1) and each of the p-th roots of unity with equal probability q/(p(q+p-1)). This generalises the work of Kurlberg and Rudnick who considered the same limit for hyperelliptic curves (i.e. cyclic 2-fold covers). We also show that when both the genus and q go to infinity, the normalized trace has a standard complex Gaussian distribution. This is joint work with A. Bucur, B. Feigon and M. Lalin.

Room Reservation Information

Room Number:MB106
Date:12 / 10 / 2009
Time:11:15am - 12:05pm