I understand that we call a “simple zero” if the first derivative of the complex function $\neq 0$. How does this apply to the zeros of the Riemann zeta? I read that all known zeros are simple. Taking the derivative of $\zeta(s) = \sum n^{-s}$ won’t work because this zeta is valid only for $\oper...

Let the $k$th shopper $k = 1..N$ skip the $v$th store they visit if and only if $v \neq \pm 1 \pmod {p_{k + 2}}$. In other words shopper $k =1$ will start at node $0$ (blue in picture) which is the Hexagon Mall entrance together with shopper $k=2$ (orange in picture). Shopper $1$ moves in patt...

I recently asked a question about whether a stochastic process $X =(X_n)_n$ could exhibit two properties at the same time, namely that $P(\sup_n X_n < \infty) = 1$ while $E(X_n) \to \infty$ as $n\to \infty$. I had a specific example in mind, but feedback I received on that question made me realiz...