13 problems

Bessel common-zero conjecture. If $f$ and $J_\alpha$ share a common zero in $\mathbb C^*$, then

For $n\in\mathbb{N}_0$ and $m\in\mathbb{N}$, let $j_{\nu,m}^{(n)}$ denote the $m$th positive zero of the $n$th derivative $J_{\nu}^{(n)}$ of the Bessel function of the first kind.…

Let $J_\nu^{(k)}(x)$ denote the $k$-th derivative with respect to $x$ of the Bessel function of the first kind of order $\nu$. For every $n\in\mathbb{N}$, consider its positive zer…

Irreducible common-zero conjecture. If $h_1$ and $h_2$ have at least one common zero in $\mathbb C$, then

Jossen's factorization conjecture. Every non-zero $E$-function $f$ can be written as a finite product of powers of $E$-functions with simple zeros, with distinct factors having no…

Multiplicity factorization conjecture. Multiple zeros of $f$ always occur for a trivial reason: the zeros of multiplicity $j$ are exactly the zeros of an $E$-function $g_j$ such th…

Uniqueness conjecture. The spectral values $\tilde{q}_1$ and $v_{\pm}$ are the only spectral values of $\theta$ for

Let ${}_pF_q(\boldsymbol{a};\boldsymbol{b};z)$ be the generalized hypergeometric function, with $p<q$, positive denominator-parameter vector $\boldsymbol{b}>0$, and numerator and d…

Let $n\in\mathbb{N}_0$, let $\nu\in\mathbb{R}$, and define the real entire function … A Fourier critical point of a real entire function is a point at which some derivative has a c…

Let $n\in\mathbb{N}_0$. For a real parameter $\nu$, write $J_{\nu}^{(n)}$ for the $n$th derivative of the Bessel function of the first kind with respect to its argument. Generalize…

Shifted-path conjecture. Each path of zeros of ${\mathfrak G}(z,t)$ representing $[{cal D}(\alpha,\beta)]^t|g\rangle$ is a shifted version, in both the real and imaginary direction…

Let $\{z_n\}$ be a sequence of complex numbers in order of nondecreasing absolute value satisfying the zero conditions referenced in the paper and … Here $\alpha$ and $\gamma$ are…

Let $F$ be an exponential integral function as defined in the paper, and let $s_nF$ denote its normalized sections. Let $D_{a,b}$ and $D_\text{imag}$ be the curves introduced in th…