All Questions

Property of any odd number of nonnegative integers: Given $x_1 \leq \cdots \leq x_{2n + 1}$ with each $x_i \in \mathbb{Z}_{\geq 0}$, suppose that for any $x_i$ we remove, the remaining numbers can be ...

It seems a marvel when a bunch of irrational numbers "conspire" to become rational, even better an integer. An elementary example is $\prod_{j=1}^n4\cos^2\left(\pi j/(2n+1)\right)=1$. Kasteleyn's ...

The Riemann xi function $\xi(s)$ is defined as $$ \xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s). $$ It is an entire function whose zeros are precisely those of $\zeta(s)$. Since $\xi$ is real ...

I think the usual proof for the asymptotic number of zeros of the Riemann zeta function $$N(T) = \#\left\{\rho : \ \zeta(\rho)=0, \begin{array}{l}\scriptstyle Im(\rho)\ \in\ [0,T]\\ \scriptstyle Re(\...