7 problems

Root-exponent bound conjecture. If $g_{\underline{r}}$ has a $k$-th root as a modular function on $X_0(\mathfrak{n})$, then

Characterization conjecture. This criterion characterizes all Drinfeld modular units on $X_0(\mathfrak{n})$.

Let $N$ be a positive integer, let $L$ be the level-dependent integer used for the Galois action, and let $\mathcal{D}_N$ and $F_{m,h}$ be the indexing set and modular-unit basis i…

Let $N>2$, and let $X_1(N)$ be the modular curve over $\mathbb{Q}$ parametrizing elliptic curves with a point of order $N$. Write $\mathbb{Q}(X_1(N))^*$ for its multiplicative grou…

Let $K$ be an imaginary quadratic field, let $\mathfrak{f}$ be a nonzero proper integral ideal of $K$, and let $K_{\mathfrak{f}}$ be the ray class field of $K$ modulo…

Let $N$ be a positive integer, let $n=\lfloor N/2\rfloor$, and let $X_1(N)$ be the modular curve. For $2\le k\le n+1$, let $f_k$ be the modular units defined in the source, and let…

Let $X_1(N)$ be the modular curve, and let $f_k$ denote the modular unit obtained from the equation for $X_1(k)$. Modular-unit generation conjecture. The modular units of…