Projections in rotation algebras and theta functions

For each α ∈ (0, 1), A_α denotes the universal C*-algebra generated by two unitaries u and v, which satisfy the commutation relation uv = e^2πiαvu. We consider the order four automorphism σ of A_α defined by σ(u) = v, σ(v) = u^-1 and describe a method for constructing projections in the fixed point algebra A^σ _α, using Rieffel's imprimitivity bimodules and Jacobi's theta functions. In the case α = q^-1, q ∈ Z, q ≥ 2, we give explicit formulae for such projections and find a lower bound for the norm of the Harper operator u + u* + v + v*.