## Speaker:

Professor Haruzo Hida

## Institution:

UCLA

## Time:

Thursday, October 14, 2004 - 4:00pm

## Location:

MSTB 254

It is a classical problem to determine the span

of the theta series of a given quadraic space over

a small ring. In such a way, Jacobi proved his

famous formula of the number of ways of expressing

integers as sums of four squares.

For the norm form of a definite quaternion algebra B,

we determine the span integrally over very small ring

(for example, if B only ramifies at one prime p,

we shall determine the span over Z[1/(p-1)]).