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Results tagged with riemann-zeta-function
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user 40906
The Riemann zeta function is the function of one complex variable $s$ defined by the series $\zeta(s) = \sum_{n \geq 1} \frac{1}{n^s}$ when $\operatorname{Re}(s)>1$. It admits a meromorphic continuation to $\mathbb{C}$ with only a simple pole at $1$. This function satisfies a functional equation relating the values at $s$ and $1-s$. This is the most simple example of an $L$-function and a central object of number theory.
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What is the behavior of the argument of Riemann’s Zeta function on other verticals inside th...
What is known about the behavior of the argument of Riemann’s Zeta function on other verticals inside the critical strip apart from the critical line ? Are there any omega type theorems in this case, …
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Who formulated the conjecture that the set of real parts of zeros of the Riemann zeta functi...
Does anyone know who formulated this conjecture related to Riemann's zeta function?
Conjecture. The set $$\{ x : \exists y \space \space \zeta (x+iy) = 0\}$$ is dense in $[0, 1]$.
In othe …
3
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Does the Riemann Xi function possess the universality property?
Here is the question.
Does the Riemann Xi function possess the universality property, or something similar to Voronin's universality property?
Here is why the answer to this question is important. …