10 problems

Assume the notation $N_0'(T)$, $N_1(T)$, and $N_2(T)$ denotes the counting functions up to height $T$ for zeros of $\zeta'(s)$ of types $0$, $1$, and $2$, respectively. Stopple's z…

Fiori–Gonek–Hughes conjecture. The size of this error satisfies

Minimum-support conjecture. The minimum number of nonzero coefficients needed for a polyanalytic polynomial of degree $n$ to have the maximum number of $n^2$ zeros is $n$.

Let $F$ be the stationary Gaussian process under consideration, let $\mu$ be its spectral measure, and let $N_F(T)$ denote its number of zeros in the interval of length $T$. Suppos…

Let $F$ be the stationary Gaussian process under consideration, let $u$ be its spectral measure, and let $NF(T)$ denote its number of zeros in the interval of length $T$. Assume t…

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 $N(T)$ denote the number of zeroes in an interval of length $T$ of a non-degenerate stationary Gaussian process (SGP), with covariance function $r$ and parameter $\sigma$ as in…

Let $p(z)$ and $q(z)$ be complex analytic polynomials of degrees $n$ and $m$, respectively, with $m<n$. The harmonic polynomial $p(z)-\overline{q(z)}$ has at most $n^2$ zeros. When…

Let $f$ be a polynomial system, let $\kappa(f)$ denote its condition number, and let the zero counting problem for $f$ be the problem of computing the number of its real zeros. Com…

Consider equilibria of the regularized Ericksen model on $[0,1]$, and let $k$ be the parameter appearing in the condition below. An internal zero is a zero in the interior of the i…