12 problems

The p-adic Brauer–Siegel conjecture. There exists a constant ${\mathcal C}_p({\mathcal K})$ such that

Tsfasman–Vladuts conjecture. One has

Tsfasman–Vlăduț conjecture. For every asymptotically exact family $\mathcal{K}$,

Let $\mathcal{K}=\{K_i\}_{i\in\mathbb{N}}$ be an asymptotically exact family of number fields. For each $i$, let $h_{K_i}$ be the class number, $R_{K_i}$ the regulator,…

Hindry–Pacheco Conjecture 1.7. The liminf of the Brauer–Siegel ratios of these quadratic twists is

Let ${\mathcal K}_{\rm real}$ be the set of all totally real number fields, let $D_K$ be the discriminant of $K$, and fix a prime $p\geq 2$. For each $K$, let ${\mathcal T}_K$ be t…

Fix a prime $p\geq 2$ and an integer $a\geq 1$ with $p\nmid a$. For integers $\rho\geq 2$ such that $m=a^2p^{2\rho}+1$ is squarefree, let … and let ${\mathcal T}_K$ be the torsion…

Let $\{E_i/K_i\}$ be an asymptotically very exact family of elliptic curves over function fields. Let $c_{E_i/K_i}$ be the leading coefficient of the $L$-function at $s=1$, let…

Let $X$ be the curve with function field $K$, and let $\{E_i/K_i\}$ be a family of elliptic curves obtained by base change. Write $g_{K_i}$ for the genus of the function field…

Let $K$ be a fixed function field and let $E_i$ be a family of pairwise non-isomorphic elliptic curves over $K$. For each $E_i$, let $c_{E_i/K}$ be defined by the leading term of i…

Let $K$ be the function field in the preceding setting, and let $T=T_0\times_{\mathbb F_q}K$, where $T_0$ is a fixed $\mathbb F_q$-torus. Put $d=\dim T$,…

Let $E$) be an elliptic $K$-curve with elliptic surface $f\colon\mathcal E\to X$, contained in an infinite Galois tower as described in the source. For each $v\in X$, let…