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Results tagged with riemann-zeta-function
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user 135926
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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Heuristic argument for the Riemann Hypothesis
Bombieri reviews the evidence for the Riemann hypothesis in his problem description for the Millenium prize. In section III, he gives the numerical evidence as one of three pieces of evidence, the sec …
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