7 problems

Anatomy-of-integers conjecture. For a fixed integer $s\geqslant 1$ and any integers $2\leqslant h<u$, we have

Jacobi-symbol conjecture for $c_p$. For any odd prime $p$,

Let $p>p_0$ be prime, assume the distinct-factor bound conjecture and the uniform-distribution conjecture, and write … where $q_1<\cdots<q_k$ are the prime factors and…

Let $p$) be an odd prime, let $\varepsilon_p$ be the fundamental unit of $\mathbb{Q}(\sqrt{p})$, and let $h(p)$ be the class number of $\mathbb{Q}(\sqrt{p})$. Write … with…

Cohen–Sun–Vsemirnov's conjecture. The number $S(1,p)/a$ is an integral square.

Let $p$ be an odd prime, let $0\leq\alpha\leq\frac{1}{2}$, and define … where $\left(\frac{n}{p}\right)$ is the Legendre symbol. Majority nonnegativity conjecture. For every…

Let $p$ be an odd prime, and let $E_p^+$ and $E_p^-$ be the convex $(p+1)$-near-edges associated respectively to the sequences of Legendre symbols and their negatives. Let…