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Results tagged with riemann-zeta-function
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user 314236
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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A paper by Viggo Brun
Does any one know a digital link to Viggo Brun's paper: "Deux transformations elementaires de la fonction Z de Riemann" Revista Ci. Lima 41 (1939), 517-25. ??
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Jacobi's original reference in Riemann's paper
In Riemann's original paper on the zeta function, page 3, he uses a result by Jacobi, and gives as reference: "Fund. S. 184".
Could someone provide a digital link, or exact reference, for this result? …
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Spiralling cycles surrounding zeros
The following came up, as a vague idea, in dialogue with a bright, female, 20 year old student of mine. It is a bit vague, but it seems that conjecture 1 is not present in the literature, which seems …
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Accepted
Bounds for analytic circles
It looks like @boJonsson made a typo, mixing up $\xi(s)$ with $\Xi(t)$, defined, for $s=1/2+it$, as:
$$\Xi(t) = \frac{1}{2} s(s-1) \pi^{-\frac{s}{2}} \Gamma\left(\frac{s}{2}\right) \zeta(s)$$
All the …
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