On Expressions of Theta Series by η-products

In this paper, we give a certain identity between an eta-product of weight 1 and theta series associated with a pair of binary quadratic forms. We also have explicit description of Siegel's theorem by an eta-product. For quadratic forms Q(1) and Q(2) which are in the same genus, we express the difference upsilon(Q1) (tau) - upsilon(Q2) (tau) by an eta-product.