  We give an algebraic analog of the functional equation of Riemann's theta
function. More precisely, we define a `theta multiplier' line bundle over the
moduli stack of principally polarized abelian schemes with theta characteristic
and prove that its dual is isomorphic to the determinant bundle over the moduli
stack. We do so by explicitly computing with Picard groups over the moduli
stack. This is all done over the ring R=Z[1/2,i]: passing to the complex
numbers, we recover the classical functional equation.
