3 problems

Algebraicity conjecture. If all Fourier coefficients of the holomorphic part of $\tilde f$ are algebraic, then $\xi(\tilde f)$ is either a unary theta series with…

Let $m>0$ and let $f$ be a harmonic weak Maass form of weight $\frac{1}{2}-m$ for the representation $\rho_L$. Assume that $\xi_{\frac{1}{2}-m}f$ is holomorphic also at $\infty$, a…

Let $\Delta$ and $r$ be as in the preceding notation, let $E_\Delta$ be the corresponding elliptic curve with minimal Weierstrass model $W_\Delta$, and let…