17 problems

Let $J_{E}^{+}[\tau]$ denote the construction in the source applied to RM points, and let a ring class field be the corresponding class field. Caiero–Darmon Conjecture 7. The image…

Fix $d\in\mathbb Z_{>0}$, $d\neq3$, write $\Delta=\Delta_d=(d+1)(d-3)=f^2\Delta_0$ with $\Delta_0$ a fundamental discriminant, and let $\mathcal M(f')$ be the multiplet indexed by…

Let $u\in S_d$, write $\nu=u^{1/3}$, and let $c=c(u)$ be the product of the distinct rational primes dividing $u$ but not $d$. Let $M_{3c}$ denote the ring class field associated w…

Let $u\in S_d$, write $\nu=u^{1/3}$, and let $c=c(u)$ be the product of the distinct rational primes dividing $u$ but not $d$. Let $c'$ be the odd part of $c$. Let…

Let $d$ be as in the paper, let $\mathcal{O}(d)$ be the associated quadratic order, and let $P_d$ and $R_d$ be the subsets defined there. For $\beta\in\mathcal{O}(d)$, let…

Let $d$ be as in the paper, let $F=\mathbb{Q}(\sqrt{-3d})$, and let $M$ and $M_3$ denote the ring class fields of $F$ for the orders used in the paper, with $M_3$ corresponding to…

Let $\theta$ be an algebraic number with minimal polynomial … where the integers $a_i$ are non-negative. Let $\varepsilon$ be a unit of the splitting field of … If…

Let $F$ be a totally real number field of narrow class number $1$, let $\mathfrak p$ be a prime of $F$, and let $K_i/F$ be quadratic extensions in which $\mathfrak p$ is inert, wit…

Let $F$ be a totally real number field of narrow class number $1$, let $\mathfrak p$ be a prime of $F$, and let $K_1,K_2$ be almost totally complex quadratic extensions of $F$ in w…

Let $F$ be a totally real number field of narrow class number $1$, let $\mathfrak p$ be a prime of $F$, and let $K/F$ be an almost totally complex quadratic extension in which…

Let $p$ be a prime number, let $v_p:4^*\to\mathbb{Z}$ be the usual $p$-adic valuation, and let $D=-3f^2$ be a discriminant. Let $j_D$ be any singular modulus relative to $D$, and l…

Let $l>3$ be a prime with $l\equiv 3\pmod{4}$, let ${\mathsf{k}}=\mathbb{Q}(\sqrt{-l})$, and let $p$ be a prime that is non-split in ${\mathsf{k}}$. Let $\mathfrak{P}_0\mid p$ be t…

Let ${\mathsf{k}}$ be an imaginary quadratic field with class number $h_{\mathsf{k}}$, and let $\mathsf{H}_{\mathsf{k}}$ be its Hilbert class field with class number…

Let $\uptheta\in\mathbb R-\mathbb Q$ be a fundamental quadratic unit and let $K=\mathbb Q(\uptheta)$, with fundamental discriminant $D$. The multivalued quantum modular invariant…

Let $Y$ be an Enriques surface whose universal cover $X$ is a singular K3 surface. Let $d<0$ denote the discriminant of $X$, and let $H(d)$ and $H(4d)$ denote the corresponding rin…

Let $Y$ be an Enriques surface whose universal cover $X$ is a singular K3 surface. Let $d<0$ denote the discriminant of $X$, and let $H(d)$ be the ring class field associated with…

Let $\goth K$ and $\Phi$ be as in the paper, let $\goth K^{\mathrm{ref}}$ be the reflex field, and assume that there is only one point over $\infty\in\mathbb P^1(F_q)$ in…