8 problems

Let $\nu$ be the Cantor measure used in the paper and let $\widetilde\nu$ be its pushforward to $(0,1)$. Let $\zeta(s,\alpha)$ denote the Hurwitz zeta function. Cantor-weighted Hur…

Equivalent Chowla–Milnor formulation. One has

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 $k\in\mathbb{N}$ and let $0<\alpha\leqslant 1$ be irrational. Write $\zeta(s,\alpha)$ for the Hurwitz zeta function and let $d$ denote the algebraic degree of an algebraic numb…

Let $p$ be a prime, let $k>1$ be an integer, and let the Hurwitz zeta function be … for $0<x\le1$. Milnor's conjecture. The real numbers … are linearly independent over…

Let $q$ and $k$ be positive integers greater than one. Consider the Hurwitz zeta values $\zeta(k,a/q)$ for integers $a$ satisfying $1\le a\le q$ and $(a,q)=1$. Milnor's conjecture.…

Hurwitz zeta moment conjecture. For every fixed real number $k>0$, there is a constant $c_k(\alpha)$ such that

Let $\alpha$ be a parameter with $0<\alpha<1/2$ or $1/2<\alpha<1$, and let Theorem 1 denote the universality statement for the Hurwitz zeta-function in the preceding theorem. Hurwi…