14 problems

The characterization of Eisenstein-type forms. The subspace of $M_{a,b}(\operatorname{SO}(\Lambda),\vartheta_d)$ spanned by forms of Eisenstein type is the span of constant functio…

Let $\Theta_f$ be a theta block of $q$-order one that is a holomorphic Jacobi form of integral weight $k$ and integral index $N$ for $A_1$. Let $\operatorname{Grit}(\Theta_f)$ deno…

Let the pure theta block $\Theta_f$ be a holomorphic Jacobi form of weight $k$ and index $m$ with vanishing order $1$ in $q$, where $k,m\in\mathbb Z_{>0}$. Define the nearly holomo…

Let $\Theta\in J_{k,t}$ be a theta block with trivial character and with order of vanishing $1$ in $q$. Here $J_{k,t}$ denotes the space of Jacobi forms of weight $k$ and index $t$…

Let $A$ range over isogeny classes of abelian surfaces over $\mathbf{Q}$ of conductor $N$ with $\operatorname{End}_{\mathbf{Q}} A=\mathbf{Z}$. Let $K(N)$ be the paramodular group ……

Let $\mathcal{A}/\mathbb{Q}$ be an abelian surface of conductor $N$ with $\operatorname{End}_{\mathbb{Q}}\mathcal{A}=\mathbb{Z}$. Let $F$ be a weight $2$ cuspidal paramodular newfo…

Let $B$ be an abelian surface defined over $\mathbb{Q}$ of conductor $N$ such that $\operatorname{End}_{\mathbb{Q}}(B)=\mathbb{Z}$. A Brumer–Kramer paramodularity conjecture. There…

Let $N$ be squarefree, and let $F\in S^k(\Gamma^{\mathrm{para}}[N])$ be a Hecke eigenform that is not a Gritsenko lift. For fundamental discriminants $\ell$ and $D$ satisfying…

Twisted Böcherer conjecture.

Let $p$) be prime and let $F\in S^k(\Gamma^{\mathrm{para}}[p])^+$ be a paramodular Hecke eigenform of even weight $k$. For each fundamental discriminant $D<0$, let $A_F(D)$ denote…

Let $F\in S^k(\Gamma^{\text{para}}[p])^+$, where $S^k(\Gamma^{\text{para}}[p])^+$ is the plus space of paramodular cusp forms, and for a fundamental discriminant $D<0$ define … whe…

Let $p$ be a prime. A paramodular form here is a Hecke eigenform $F\in S^2(\Gamma^{\text{para}}[p])$ with rational eigenvalues; exclude Gritsenko lifts. Let $\mathcal{A}$ be an iso…

Let $f$ be a weight $2$ newform for the paramodular group $K(N)$, not in the span of the Gritsenko lifts. Let $k_f$ be the totally real number field generated by the Hecke eigenval…

Paramodular cohomology conjecture. The cuspidal cohomology $H^5_{\mathrm{cusp}}(\Gamma_0(N);\mathbb C)$ contains a $2d_h$-dimensional subspace spanned by Hecke eigenclasses. For ev…