7 problems

Extension-frequency conjecture. Precisely one half of unramified $[2,2]$-extensions of cyclic cubic fields extend to unramified $\langle8,4\rangle$-extensions.

Narrow/wide frequency conjecture. For each relevant $n$, the proportion of fields satisfying

Wide realization conjecture. Every finite $2$-select $2$-group arises as the wide tower group of some cyclic cubic field.

Narrow realization conjecture. Every finite $2$-special $2$-group arises as the narrow tower group of some cyclic cubic field.

Let $p>3$ be a prime, and let $M_p^{\mathrm{inert}}$ be the measured space of matrices associated with the inert case. Define the random variable … where $f=X^2+3Y^2$. Inert-case v…

Let $p>3$ be a prime. Let $\mathbb Q_p^{(3)}$ be the unique unramified cubic extension of $\mathbb Q_p$, with ring of integers $\mathbb Z_p^{(3)}$ and cyclic Galois group generated…

Let $\mathcal K$ be the set of all cyclic cubic extensions of $\mathbb Q$ in a fixed algebraic closure. For a prime $p$, let $\mathcal K_p^{\mathrm{un}}$ and…