5 problems

Cyclic cubic and quintic unit signature conjecture. As $K$ varies over cyclic number fields of degree $\ell$, the probability that the unit signature rank is $1$ is

Cyclic degree-prime unit signature conjecture. As $K$ varies over cyclic number fields of degree $\ell$ with odd class number, for $0\le s\le m$,

Cyclic cubic signature conjecture. As $K$ varies over cyclic cubic number fields, the probability that $K$ has a totally positive system of fundamental units is approximately $3\%$…

Let $L$ range over totally real fields of prime degree $p$, ordered by absolute discriminant, and let $\rho_\infty$ denote the dimension of the quotient of totally positive units b…

Let $p$ and $q=2p+1$ be primes, let $L=\mathbb Q(\zeta_q+\zeta_q^{-1})$, and let $C_L^+$ denote the narrow class group of $L$, with $C_L^2$ its subgroup of squares. Define … where…