15 problems

Consider the $34$ ternary lattices listed in the theorem immediately preceding the conjecture, over the relevant real quadratic fields. A universal ternary lattice is a ternary qua…

Let $D$ be a positive squarefree integer, let … and let $\mathcal{O}_F$ denote the ring of integers of $F$. A universal ternary $\mathcal{O}_F$-lattice is a universal quadratic lat…

Let $\beta\in\mathbb R$ satisfy $a\beta^2+b\beta+c=0$ with $a,b,c\in\mathbb Z$ and $b^2-4ac$ nonsquare, and let $\r\in\mathbb Q^2$. Let \shin^{\r}[\beta] and…

Let $K=\mathbb{Q}(\sqrt{D})$, where $D=pq$ with $p\equiv 5\pmod 8$ and $q\equiv 1\pmod 8$, and suppose … Assume also … Let $X_{\infty}$ be the Iwasawa module of the cyclotomic…

Class-number infinitude conjecture. There are infinitely many $r\in\mathbb{Z}^+$ such that $p$ does not divide the class number of $K_r$.

Let $f$ be a weight-$2$ newform of level $\Gamma_0(p)$ with integer Fourier coefficients, let $E=E_f$ be the associated elliptic curve with multiplicative reduction at $p$, and let…

Let $p$ be a prime, let $\tau\in\mathcal{H}_p$ be a real quadratic point of discriminant $D$ prime to $p$, and let $H_\tau$ be the narrow ring class field of the order defined by…

Let $K$ range over real quadratic fields, with regulator $R_K$, discriminant $d_K$, and parameter $m_K$ as used in the source. Regulator-growth conjecture. There exists an infinite…

Let $N$ be a level, let $E$ be a real quadratic field, and let $\psi_{\Gamma,E}$ denote the map associated with a subgroup $\Gamma$ as in the conjecture. Write $A_E(N)$ and…

Fix an integer $c$ prime to $D\cdot N$, let $\mathcal{O}_c$ be the order of the real quadratic field $F$ of conductor $c$, and let $Q\in\mathcal{F}_{Dc^2}$ represent a class of qua…

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 $D$ be a positive nonsquare integer, let $\mathbb Z[\sqrt D]$ be the quadratic order, and let $N$ be the minimum of the absolute values of negative norms of elements of…

Greenberg's rationality conjecture. The local point $P_\psi$ is a global point, and more precisely

Twisted Teichmüller curve uniqueness conjecture. Suppose $D\equiv 5\pmod 8$ is a fundamental discriminant with narrow class number $h_D^+=1$. For every $n\ind4aa_D$, all matrices

Let $[(r,\tau)]\in(\mathbb{Z}/f\mathbb{Z}\times H^{\mathcal{O}}(\mathfrak{N}))/\sim_f$ with $\tau$ reduced, set $\mathcal{O}=\mathcal{O}_{\tau}$, $\mathfrak{f}=f\mathcal{O}$,…