Number Theory Seminar

I will talk about cuspidal automorphic representations of
GL(n) over Q which are unramified at all finite places, self-dual up to
twist, and algebraic regular. I will explain how to count the number of
those representations as a function of their weights -- or archimedean
component -- for all n<9 (in a weak sense when n=7). In particular, this
gives explicit conjectural formulas for the number of polarized regular
pure motives over Q with good reduction everywhere, of any rank n as
above, and of arbitrary given real Hodge structure. (Joint with D.
Renard)