1 research outputs found
The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms
From a result of Waldspurger, it is known that the normalized Fourier
coefficients of a half-integral weight holomorphic cusp eigenform \f
are, up to a finite set of factors, one of when
is square-free and 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 ? In particular, if we look at the set of
with 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