5 problems

Let $m$ and $n$ be in the critical range for the algebraic Hecke character $\psi_m$, and define … Suppose a prime $\ell>m$ divides the denominator of $Q(m,n)$. Harder's conjecture.…

Let $k>0$ and $l\geq0$ satisfy $k\equiv_6 l$. Let $\mathcal X^{(2)}_{\Gamma[\sqrt{-3}]}$ be the genus-2 moduli space considered in the paper, let $\mathbb W_{k,l}$ be the correspon…

Let $j,k,l\geq0$, let $\nu$ be a Hecke parameter, and let $\mu\vdash4$ be a partition indexing an $\mathfrak S_4$-isotypic component. The modular-9 trace congruence conjecture. … T…

Let $E_c(\lambda)$ and $E_{\rm extr}(\lambda)$ be the representations obtained from the compactly supported Euler characteristic and the extraneous contributions, respectively. Let…

Let $\lambda\neq(0,0,0)$, let $\nu$ and $\mu$ be as in the paper, and write $\lambda=(a,b,i)$ so that $i\equiv_2 a+b$. Let $T(\nu)$ be the Hecke operator, $F_\nu$ the corresponding…