From a result of Waldspurger, it is known that the normalized Fourier
coefficients a(m) of a half-integral weight holomorphic cusp eigenform \f
are, up to a finite set of factors, one of ±L(1/2,f,χm​)​ when
m is square-free and f is the integral weight cusp form related to \f by
the Shimura correspondence. In this paper we address a question posed by
Kohnen: which square root is a(m)? In particular, if we look at the set of
a(m) with m square-free, do these Fourier coefficients change sign
infinitely often? By partially analytically continuing a related Dirichlet
series, we are able to show that this is so