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Results tagged with riemann-zeta-function
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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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Is the imaginary part of $\displaystyle\ \zeta(s)\zeta(1-s)=0$ for $\operatorname{Re}(s)=\fr... [closed]
Some of my computations here showed to me that the imaginary part of $\displaystyle\ \zeta(s)\zeta(1-s)=0$ for $\operatorname{Re}(s)=\frac{1}{2}$, really i w'd like to know if there is any paper showe …
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Does there exist a rational polynomial $P(x)\in{\mathbb Q}[x]{}$ such that $P(\zeta(s))=\zet...
let $P(x)\in{\mathbb Q}[x]{}$ be a rational polynomial with $P(1) >1$ and $\zeta $ be the Riemann zeta function , I want to know if there exist a rational polynomial such that $P(\zeta(s))=\zeta(P(s)) …
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What is the approximation of $\log(|\zeta'(\frac{1}{2}+it)|)$ in Dirichlet polynomial if it ...
I have done some search many times on web to find any approximation of $\log|(\zeta'(s))|$ in Dirichlet polynomial but I didn't got it, Probably that $\log(|\zeta'(s)|$ dosn't have a Dirichlet poly …
2
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Is $|\zeta(e^{ni})|\leq \log(n)$ true for $n > 19$ and how do i can show it if it is?
I performed some computations in wolfram alpha looking at the behavior of the values of $|\zeta(e^{ni})|$ trying to predict a lower bound. I have got the following result:
For $n > 19 :|\zeta(e^{ni}) …
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Could the Riemann zeta function be a solution for a known differential equation?
Riemann zeta function is a function of complex variable $s$ that analytically continous the sum of Dirichlet series .defined as :$$\zeta(s)=\sum_{n=1}^{\infty}\displaystyle \frac{1}{n^s} $$ for when t …
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if $\max_{z \in K} |\zeta(z+it)-f(z)|<\epsilon.$ then is this $\lim_{t\to \infty} \inf \frac...
Universality theorem of Riemann zeta function states that :Let $K$ be a compact subset with connected complement lying in the strip $\{1/2 < \operatorname{Re}(z)<1\}$, and let $f : K \rightarrow \math …
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Any simplification of this inequality if it is true? :For $t\geq 1.22$: $|\zeta(0.5+it)|\leq...
When I tried to give bounds for $\zeta(0.5+it)$ using some transformations over Gamma function using the function $f(x)=\exp(-n x)$ over the range $(0,+\infty)$ , For $ Re(s)=\frac12 $ and $t >0$ I …
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Could the complex zeros of Riemann zeta function be of the form $ s=0.5+ik$ with $k$ a posit... [closed]
I have checked in Andrew Odlyzko, Tables of zeros of the Riemann zeta function, to know if there is an example of zeros of Riemann zeta function with integer imaginary parts, but I don't see that. I w …