4 problems

Let $n$ be an odd prime. For $1\leq\kappa\leq n-1$, define … where $r(j,n)$ is the unique integer congruent to $j$ modulo $n$ in $\{-(n-1)/2,\ldots,(n-1)/2\}$. Kazashi and Sloan's…

Let $N\ge 3$ be prime and let $R_N^+:=\{1,2,\ldots,(N-1)/2\}$. For $\kappa\in R_N^+$, let $T_N(\kappa)$ be the quantity defined in the source, and order the elements as…

Let $z$ and $N$ be integers with $\gcd(z,N)=1$. Let $B_1$ and $B_2$ denote the first and second Bernoulli polynomials, respectively, and interpret $z(k-\ell)\bmod N$ as the residue…

Let $d$ be the dimension, and let … on the dimension $d$ is inevitable and cannot be improved by alternative steps in the proof. This conjecture concerns the sharpness of the dimen…