It is not the function that takes particular values, the (nontrivial) zeros of the function (probably) occur at particular values.mustang19 said:Specifically, has anyone proven that the real part of a result of some particular function always assumes a particular value?
The Riemann hypothesis is a conjecture in mathematics that was proposed by Bernhard Riemann in 1859. It states that all non-trivial zeros of the Riemann zeta function lie on the critical line of 1/2 in the complex plane.
The Riemann hypothesis is considered one of the most important unsolved problems in mathematics. Its solution would have far-reaching implications in various fields of mathematics, such as number theory, analysis, and physics. It is also closely connected to the distribution of prime numbers.
No, the Riemann hypothesis remains unsolved to this day. Many mathematicians have attempted to prove or disprove it, but no one has been able to provide a definitive answer.
Since its proposal, there have been many attempts to prove or disprove the Riemann hypothesis. Some mathematicians have made significant progress and discovered new connections and results related to the hypothesis, but no one has been able to provide a definitive proof or disproof.
If the Riemann hypothesis were to be proven true, it would have a significant impact on many areas of mathematics, including number theory, analysis, and physics. It would also lead to the development of new mathematical techniques and potentially solve other long-standing problems in mathematics.