Dihua Jiang (Minnesota)

The well-known conjecture of P. Deligne (1979) explains the periods and critical values for motivic L-functions. In 1997, D. Blasius explicates the same conjecture for automorphic L-functions of motivic type. The special case of those conjectures for the Riemann zeta function goes back to the classical Euler formula. In this talk, we explain how to reformulate the Friedberg-Jacquet integral in terms of local and global modular symbols and continuous cohomology when the automorphic representations of  are algebraic and regular and how to prove the Blasius-Deligne conjecture for by proving the non-vanishing hypothesis of A. Ash and D. Ginzburg (1994) and other arithmetic results associated with the local Friedberg-Jacquet integrals.