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- W4229588246 abstract "The basic idea is to expand the completed zeta function $xi(s)$ in MacLaurin series (infinite polynomial). Thus, by $xi(s)=xi(1-s)$, we have the following infinite polynomial equation begin{equation}nonumber begin {split} &xi(0)+xi^{'}(0)s+frac{xi^{''}(0)}{2!}s^{2}+cdots+frac{xi^{(n)}(0)}{n!}s^{n}+cdots =&xi(0)+xi^{'}(0)(1-s)+frac{xi^{''}(0)}{2!}(1-s)^{2}+cdots+frac{xi^{(n)}(0)}{n!}(1-s)^{n}+cdots end {split} end{equation} which leads to $s=1-s$ with solution $s=alpha pm jbeta = frac{1}{2} pm jbeta$. It is obvious that the zeros of $xi(s)$ are determined by $xi(s)=xi(1-s)=0$ which is a special case of $xi(s)=xi(1-s)$. Thus a proof of the Riemann Hypothesis can be achieved." @default.
- W4229588246 created "2022-05-11" @default.
- W4229588246 creator A5080014014 @default.
- W4229588246 date "2021-09-22" @default.
- W4229588246 modified "2023-10-18" @default.
- W4229588246 title "A Proof of the Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function" @default.
- W4229588246 doi "https://doi.org/10.20944/preprints202108.0146.v6" @default.
- W4229588246 hasPublicationYear "2021" @default.
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