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تسجيل مستخدم جديدA Simple Solution to a Major Problem: Proof of the Riemann Hypothesis
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Fayang Qiu
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Starting from the symmetrical reflection functional equation of the zeta function, we have found that the sigma values satisfying zeta(s) = 0 must also satisfy both |zeta(s)| = |zeta(1 - s)| and |gamma(s/2)zeta(s)| = |gamma((1 - s)/2)zeta(1 - s)|. We have shown that sigma = 1/2 is the only numeric solution that satisfies this requirement.
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In this article, we will prove Riemann Hypothesis by using the mean value theorem of integrals. The function $ xi(s) $ is introduced by Riemann, which zeros are identical equal to non-trivial zeros of zeta function.The function $ xi(s) $ is an entire
function, and its real part and imaginary part can be represented as infinite integral form. In the special condition, the mean value theorem of integrals is established for infinite integral. Using the mean value theorem of integrals and the isolation of zeros of analytic function, we determined that all zeros of the function $ xi(s) $ have real part equal to$frac{1}{2}$, namely, all non-trivial zeros of zeta function lies on the critical line. Riemann Hypothesis is true.
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The Riemann hypothesis, conjectured by Bernhard Riemann in 1859, claims that the non-trivial zeros of $zeta(s)$ lie on the line $Re(s) =1/2$. The density hypothesis is a conjectured estimate $N(lambda, T) =Obigl(Tsp{2(1-lambda) +epsilon} bigr)$ for a
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