5 problems

Pisot characterization conjecture. One has $l_n(q)>0$ if and only if $q$ is a Pisot number.

Bounded $q$-expansion conjecture.

Let $f_{l,w}$ be the normalised extremal quasi-modular form of weight $w$ and depth at most $l$, and let … be the set of weights for which its Fourier coefficients are integral. In…

Let $H$ be the entropy function and let ${\mathcal{E}}$ denote the exceptional set introduced in the paper. By Theorem 2, $H$ is differentiable inside each entropy plateau…

Let $N$ be square-free, let $g>0$ be the genus of the moonshine modular curve associated to the group $\Gamma_0(N)^+$, and consider its function field. Integral generators conjectu…