6 problems

Let $a_n(k)$ denote the coefficient of $x^k$ in the cyclotomic polynomial of order $n$, let $\delta(a_n(k)=v)$ denote the density of integers $n$ for which this coefficient equals…

Hayman's conjecture. The differential polynomial $f^n f'$ cannot have any non-zero generalized Picard exceptional values.

Let $S\subset\mathbb{C}$ be Borel, and let $\zeta(s,\alpha)$ denote the Hurwitz zeta function for a shift parameter $0<\alpha<1$. Gaussian value-distribution conjecture. For large…

Let $J\geq2$, and let $f_j$, $1\leq j\leq J$, be pairwise orthogonal real-valued Hecke–Maass cusp forms for $\operatorname{SL}_2(\mathbb{Z})$, with spectral parameters $t_{f_j}$. A…

Symmetry conjecture. For $x>0$ and sufficiently small $\delta>0$,

Radziwiłł's Gaussian value-distribution conjecture. If $V=o(\sqrt{\log\log T})$ as $T\to+\infty$, then