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Institute for the Physics and Mathematics of the UniverseWPI

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: