## IPMU Komaba seminar

Date: | July 28, 2008, 17:00 - 18:30 |

Place: | Room 002, Mathematical Sciences Building,
Komaba Campus, The University of Tokyo |

Speaker: | Lin Weng (Kyushu University) |

Title: | Symmetries and the Riemann Hypothesis |

Abstract: |
Associated to each pair of a reductive group and its maximal parabolic, we will introduce an abelian zeta function.
This zeta, defined using Weyl symmetries, is expected to satisfy a standard functional equation and the Riemann Hypothesis.
Its relation with the so-called high rank zeta, a very different but closely related non-abelian zeta, defined using stable lattices and a new geo-arithmetical cohomology, will be explained.
Examples for SL, SO, Sp and G_2 and confirmations of (Lagarias and) Masatoshi Suzuki on the RH for zetas associated to rank 1 and 2 groups will be presented as well. The manuscript is available at: http://xxx.lanl.gov/abs/0803.1269 |