Clifford Algebras and Shimura's Lift for Theta-Series, by Fedor Andrianov

In this paper we use automorph class theory formalism to construct a lifting of similitudes of quadratic Z-modules of arbitrary ternary nondegenerate quadratic forms to morphisms between certain subrings of associated Clifford algebras. The construction explains and generalizes Shimura's correspondence in the case of theta-series of positive-definite quadratic forms. Relations between associated zeta-functions are considered.

Fedor Andrianov <fedandr@math.uchicago.edu>