6 problems

Sharpness conjecture. The exponent $3/2$ in the upper bound

Let $N_R$ denote the number of zeros of a Gaussian process on an interval whose length grows with $R$, and consider the higher central moments of $N_R$. Higher central-moment asymp…

Let $\mathcal{Z}(y)$ denote the Hardy-type real-valued normalization of the Riemann zeta function on the critical line. For $h$ in the ranges specified below, consider logarithmic…

Let $u_N(t,x)$ be the truncated Wiener-chaos expansion … and let $T_p(\theta)$ be the transition time defined in the paper. For $p\geq 2$, write $\|u_N(t,x)\|_p$ for the $L^p$-norm…

BNK conjecture. The second moment $E X_n^2$ grows quadratically with $n$, and the third moment $E X_n^3$ grows cubically with $n$.

Basu–Sarkar–Ulam conjecture. The second moment $E X_n^2$ grows quadratically with $n$ as $n\to\infty$.