2 problems

Let $f$ be a half-integral-weight Hecke eigenform, and let $b(n)$ denote its normalized Fourier coefficients. Bruinier–Kohnen conjecture. The signs of the coefficients of $f$ are e…

Let $f$ be as above, let $I\subseteq\mathbb R_{>0}$ be any interval, and let $b(n)$ be the normalized coefficients of $f$. Independence of sign and absolute value conjecture. The f…