Summary: THE UNIVERSITY OF CHICAGO
CLIFFORD ALGEBRAS AND SHIMURA'S LIFT FOR THETA-SERIES
A DISSERTATION SUBMITTED TO
THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
DEPARTMENT OF MATHEMATICS
FEDOR A. ANDRIANOV
To Yuliya, who made a wonderful difference in my life.
Automorph class theory formalism is developed for the case of integral nonsingular
quadratic forms in an odd number of variables. As an application, automorph class
theory is used to construct a lifting of similitudes of quadratic Z-modules of arbitrary
nondegenerate ternary 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 ternary quadratic forms.
The relation between associated zeta-functions is considered.