All Questions

Consider the following sum of function of primes: $$-\sum_{p}\ln\left( 1 - \frac{1}{(ep)^{1/2}} \right){\ln(p)}$$ Here $p$ runs through all primes and $e$ is Euler's constant. We can see that the sum ...

( I've been thinking about asking this for a long time . Though this is not rigorous; It can be thought of as heuristic or extraction of information from different viewpoint.) We know "super-...

Consider the equation $$1 + 2 + 3 + 4 + \cdots = - \frac{1}{12},$$ "proved" by Ramanujan Euler. One correct way to interpret this is that $\zeta(-1) = - \frac{1}{12},$ where $\zeta(s) = \sum_{n = 1}^{\...