  Siegel defined zeta functions associated with indefinite quadratic forms, and
proved their analytic properties such as analytic continuations and functional
equations. Coefficients of these zeta functions are called measures of
representations, and play an important role in the arithmetic theory of
quadratic forms. In a 1938 paper, Siegel made a comment to the effect that the
modularity of his zeta functions would be proved with the help of a suitable
converse theorem. In the present paper, we accomplish Siegel's original plan by
using a Weil-type converse theorem for Maass forms, which has appeared
recently. It is also shown that "half" of Siegel's zeta functions correspond to
holomorphic modular forms.
