For more information about this meeting, contact Robert Vaughan.

Title: | Bounds of the summatory function of Moebius function in function fields |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Byungchul Cha, Muhlenberg College |

Abstract: |

We study the growth rate of the summatory function of the Moebius function
in the context of an algebraic curve over a finite field. Our work shows a
strong resemblance to its number field counterpart, which was proved by Ng
in 2004. We find an expression for a bound of the summatory function, which
becomes sharp when the zeta zeros of the curve satisfy a certain linear
independence property. Then, we consider a certain geometric average of such
a bound in a family of hyperelliptic curves, using Katz and Sarnak's
reformulation of the equidistribution theorem of Deligne. Lastly, we study
an asymptotic behavior of this average as the family gets larger by
evaluating the average values of powers of characteristic polynomials of
random unitary symplectic matrices. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 28 / 2010 |

Time: | 11:15am - 12:05pm |