5 problems

Fix an integer $d \geq 3$. For a totally real number field $K$ of degree $d$, let $\operatorname{disc}(K)$ denote its discriminant, and let an ideal class mean a class of fractiona…

Non-negligible-prime-ideal conjecture. The proportion of such coefficient vectors is inverse-polynomial in $d$ and $\log(B)$:

Let $a(\beta,\beta')$ denote the quantities appearing in Theorem, and let $\beta>0$ be real. For $\beta$ integral or half-integral, the corresponding $\beta$-moment has matching lo…

Let $K$) be a number field of bounded degree $n$ over $\mathbb{Q}$, with discriminant $D_K$ and class number $h_K$. An ideal class is said to contain a prime ideal if some prime id…

Let $G=\operatorname{cl}(\mathcal{O})$ be the ideal class group of an order $\mathcal{O}$ in an imaginary quadratic field, with cardinality $h$. Let $S_k$ be the sequence of ideal…