For more information about this meeting, contact Robert Vaughan.

Title: | Cancelled, owing to inclement weather |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Jeffery Lagarias, University of Michigan |

Abstract: |

Let F_n denote the product of all nonzero
Farey fractions of order n and let G_n denote the product
of all reduced and unreduced Farey fractions
of order n. It is known that the reciprocal of G_n is the product of binomial coefficients on the n-th row of Pascal's triangle. We present results on the growth rate of log F_n and of log G_n, and on the behavior of the p-adic norms of F_n and G_n.
The p-adic behavior of G_n is related to the Riemann zeta function on the line Re(s)=0. We present experimental results suggesting that F_n is related to behavior of the Riemann zeta function on another line. (This is joint work with Harsh Mehta (U. South Carolina).) |

### Room Reservation Information

Room Number: | MB114 |

Date: | 02 / 02 / 2015 |

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