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Results tagged with riemann-hypothesis
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user 449628
Questions about the famous conjecture from Riemann saying that the non-trivial zeroes of the Riemann Zeta function all lie on the so-called critical line $\Re(s)=\dfrac{1}{2}$, its various generalizations and the different approaches towards its solution.
3
votes
GRH and the Euler product
In general, if $F(s)$ and $G(s)$ obeys the relationship
$$
G(s)=\sum_{n\ge1}{F(ns)\over n},
$$
then Möbius inversion gives
$$
F(s)=\sum_{n\ge1}{\mu(n)\over n}G(ns).
$$
Using the power series expansion …
- 1,315
12
votes
Why is so much work done on numerical verification of the Riemann Hypothesis?
Although merely calculating the nontrivial zeros cannot lead to a direct proof of the Riemann hypothesis, these calculations are still helpful at creating numerical bounds for arithmetical functions.
…
- 1,315