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 |