Background: (required for Collatz novices and maybe well-known by Collatz experimenters) Let $f(x) = |3x + 1|_2(3x + 1) = \dfrac{3x + 1}{2^{\nu_2(3x+1)}}$ be the accelerated Collatz function, and we define (this does not match the standard definition) an odd Collatz $n$-loop to be a tuple $(x_0, ...

Let $\zeta$ denote the Riemann zeta function. My question: is $\frac{1}{\zeta(1+it)}$ bounded as $t \rightarrow \infty$ ? The motivation of my question: It seems if the answer is yes, then there exists a sequence of zeros of $\zeta$ whose real parts converge to $1$. Indeed, let $\Theta \leq 1$ b...