All Questions

Let $P$ be the prime zeta function $$ P (s) = \sum_{p\, \in\text{ primes}} \frac 1 {p^s} = \frac {1} {2^s} + \frac {1} {3^s} + \frac 1 {5^s} + \frac 1 {7^s} + \frac 1 {11^s} + \cdots $$ and define the ...

Consider the following prime sum: \begin{aligned} \sum _{p}{\frac {\cos(x\log p)}{p^{1/2}}} \end{aligned} whose spikes appear at the Riemann $\zeta$ zeros as shown here. Taking these detected spikes (...

I am wondering if it is possible to get a useful exact formula, or at least some useful asymptotics, for the partial sums of the Liouville function (OEIS sequence A002819) $$L(n)=\sum_{k=1}^n \lambda(...

I know the linked articles from Wikipedia for the Euler's totient function and the Dedekind psi function. I know that are in the literature famous, interesting and difficult problems involving the ...

Using Maple to compare $\pi^2$ and the partial sums of $6\sum_{n=0}^{\infty}\frac{1}{n^2}$ I have noticed something that appears strange. For instance, let $S_{k}=6\sum_{n=0}^{k}\frac{1}{n^2}$ be ...

Amateur math question. I was playing around generating some 2D images, and wondered what it would look like if placed $P_{i}$ dots on a circle with diameter of $i$ for increasing values of $i$, where $...