Disproved the Riemann Hypothesis?

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SUMMARY

The discussion centers on the claimed disproof of the Riemann Hypothesis, highlighting critical errors in the argument presented. Key issues include the undefined variable 'i', improper definition of 'j' regarding multiplicity, and the divergence of sums that are incorrectly equated to convergent expressions. Additionally, the assertion that the sum equals the zeta function for real values of 's' greater than 2 is proven false. These points collectively reinforce the validity of the Riemann Hypothesis as it stands.

PREREQUISITES
  • Understanding of complex analysis, particularly the Riemann zeta function.
  • Familiarity with mathematical proofs and disproofs in number theory.
  • Knowledge of convergence and divergence in series.
  • Basic grasp of mathematical notation and definitions, including multiplicity.
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  • Study the properties of the Riemann zeta function and its implications for number theory.
  • Explore convergence and divergence of series in advanced calculus.
  • Investigate the historical context and significance of the Riemann Hypothesis.
  • Learn about common pitfalls in mathematical proofs and how to identify them.
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Mathematicians, number theorists, and students interested in advanced mathematical concepts, particularly those focused on the Riemann Hypothesis and its implications in mathematics.

choe
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(Dis)proof of Riemann hypothesis,Goldbach,Polignac,Legendre conjecture

I'm just an amateur and not goot at english ^^;
 

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In your claimed disproof of the Riemann Hypothesis, introduction:

1. Line 2: i is undefined.
2. Line 3: j is not properly defined; is this counted with or without multiplicity?
3. Line 4, third equality: Since D_i is finite and the expression in the sum is constant wrt n, the sum diverges and thus is not equal to the preceding expression which is convergent for all s with Re(s) > 1.
4. Line 4, fourth equality: The sum is not equal to the zeta function for any real s > 2, which can be verified by subtracting the series. (More precise results are possible; I don't care to calculate them.)
5. Line 6: The equality is totally unjustified and usually wrong.
 

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