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Results tagged with riemann-zeta-function
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user 138096
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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How to estimate the integral of Riemann zeta function with error term trends to zero as T tr...
$\zeta(s)$ denotes the Riemann zeta function. For $T>0$ large enough $$\int_{T}^{2T}|\zeta(\frac{1}{3} + it)
\ \zeta(\frac{2}{3} + it)|dt = \ ? $$
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