Jul 23, 2010 · In laymen's terms, as much as possible: What is the Riemann-Zeta function, and why does it come up so often with relation to prime numbers?

I derive an intermediate formula for the sum for the general case of $\zeta (2k)$, then specialise to the case $\zeta (4)$ and evaluate it. Then use the formula to evaluate the general case in …

Functional equation for $\zeta$ will be quite useful when calculating those values. Of course, this equation is a part of proof that $\zeta$ can be continuated to $\Bbb {C}\setminus \ {1\}$.

I've tried googling this and surprisingly can't find much on it, even the wikipedia article for zeta function doesn't explain how this integral is derived or cite a source anywhere.

I am told that when computing the zeroes one does not use the normal definition of the rieman zeta function but an altogether different one that obeys the same functional relation. What is …

Aug 20, 2016 · But I've never really seen a detailed proof of the absolute convergence of the Riemann zeta function in the half-plane $\Re (s)> 1$. I hope there's interest on a detailed proof …

The Euler product is of little to no use in studying the zeros of the Riemann zeta function from what I know. It doesn't converge in the critical strip, for example. Its intrigue is that an object …

Closed 13 years ago. Possible Duplicate: How to evaluate Riemann Zeta function I have an amateur interest in the Zeta Function. I have read Edward's book on the topic, which is …

Aug 17, 2012 · He wrote two fundamental papers on calculating zeros on the critical line - Fast algorithms for multiple evaluations of the Riemann zeta function and Supercomputers and the …

"This formula says that the zeros of the Riemann zeta function control the oscillations of primes around their 'expected' positions." "Roughly speaking, the explicit formula says the Fourier …