6 problems

Main correspondence conjecture. There is a one-to-one correspondence between such $F$ and $G$. It has the following properties: the degree-six zeta function $L(F;s)$ equals the sta…

Let $\mathbb{K}$ be an imaginary-quadratic number field, and let $G^{(\mathbb{K})}_k$ denote the Hermitian Eisenstein series appearing above. Nonvanishing conjecture. For every eve…

Let $\boldsymbol{K}$ be the Eisenstein field, let a Hermitian theta series be associated with the Hermitian Leech lattice, and let $p$ be a prime number. Hermitian Leech-lattice th…

Hermitian Ikeda lift conjecture. The Hermitian theta series $\Theta^{(4)}(w_9)$ is a Hermitian Ikeda lift.

Let $F^{(4)}$ be the degree-four Hermitian modular form of weight $12$ defined by … The form $F^{(4)}$ is nonzero. Hermitian Ikeda-lift conjecture. The form $F^{(4)}$ is a Hermitia…

Let … The form $F^{(n)}$ is a Hermitian modular form of weight $12$; in particular, the theorem establishes that $F^{(4)}\not\equiv 0$ and that either $F^{(3)}\equiv 0$ or…