12 problems

Let $A=\mathbb{F}_q[T]$, let $\mathfrak p\trianglelefteq A$ be a maximal ideal of degree $d$, and let $n\geq 1$. For integers $k,l$, write $\mathbf{T}_{\mathfrak p}$ for the correspo…

Non-square congruence subgroup conjecture. Both $\Gamma_1(\alpha T+\beta)$ and $\Gamma_0(\alpha T+\beta)$ may be non-square congruence subgroups for any choice of $\alpha\neq 0$ an…

Let $A$ be the coefficient ring and let $T$ be the prime defining the level. For weights $k,l$, write $S_{k,l}(\mathrm{GL}_2(A))$ for the space of Drinfeld cusp forms for…

Let $A=\mathbb{F}_3[t]$, let $n\geq 2$, and set $k_n=1+3^n$. Let $\Sigma_n\subset(\mathbb{F}_3^\times)^n$ be the set of sign tuples with exactly $i$ entries equal to $-1$ for some…

Multiple Eisenstein correspondence conjecture. The following properties hold: (1)…

The correspondence conjecture. The correspondence $\zeta_A(\mathcal{C})\leftrightarrow\varphi_A(\mathcal{C})$ induces an isomorphism of $\mathbb{F}_p$-algebras

Slope multiplicity conjecture. Under these hypotheses,

The oldform and Hecke conjectures. The following assertions should hold:

Joshi–Petrov conjecture. Given $q$, there exist $k\gg 0$ and $m$, with $0\leq m<q$ and $k\equiv 2m\pmod{q-1}$, such that

Let $\mathbb{T}_{>0}$ be the algebra of power series with positive convergence radius, and let $g$, $h$, and $\boldsymbol{s}_2$ be the almost $A$-quasi-modular forms used in the so…

Let $q=p^e$ be a prime power, let $A=\mathbb{F}_q[\theta]$, and let $f$ be a non-zero Drinfeld quasi-modular form of weight $w$ and depth $l\geq 1$. Write $\nu_{\infty}(f)$ for its…

Let $f$ be a differentially extremal element of the algebra $\widetilde{M}$ of Drinfeld quasi-modular forms. A form is defined over a field $L\subset C$ if $f\in L[E,g,h]$, where…