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TheOogy
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in the Riemann Zeta function, is it possible to have two complex zeros off the critical strip that both have the same imaginary part?
TheOogy said:in the Riemann Zeta function, is it possible to have two complex zeros off the critical strip that both have the same imaginary part?
TheOogy said:i'm looking for two complex zeros that both have the same imaginary part but have diffrent real part, non with real part half. it differs from the riemann hypothesis because i don't care for a single zero off the strip, just pairs. MAYBE some one can prove that, like that dude who proved that 40% of the complex zeros have real part half or the guys who proved all the complex zeros are between 0 and 1. i also don't understand what you mean by zeta(1/4) and zeta(3/4) these are not complex and not zeros.
solamon said:What s going on here ?it s an hypothesis to be confirmed or rejected .rscosa ?no statements please about the location of the zeros.we re doing mathematics here .it s just an hypothesis then we re not allowed to consider it true.i m sorry but you have not seen what it s about yet .
solamon said:But who just said it s been proven there are no nontrivial zero off the critical line?do you have the proof reference?i would like to have a look because i have not heard yet about it.problems like this are good not for the results of the proof but they develop logic and minds ,they develop the way of walking close to the reality.
solamon said:so .who knows if zeta can be real off the critical line but on the critical strip?
Are you trying to SAY something here?solamon said:hi mate.don t look far .the Riemann hypothis is easy to prove, it can t be that hard and there might be lot of proofs .i believed it was true ,false too , false , true. but today i believe in one result .true or false ,definitly , i don t think that i will change the last result i have had ,for fun ,TO OCCUPY MYSELF MORE.
i believe that people have sorted RH since years now ,just not published , i know some mathematicians will not stuck with RH .
I NEED HISTORY ABOUT RIEMANN AND RH .EVERYTHING HE HAS SAID ABOUT IT .
BELIEVE THAT HE CAN BE WRONG HE IS A HUMAN BEING LIKE EULOR OR GAUSS WHO COULD NOT SORTED :1-1+1-1+1...=
I M LIL BIT TROUBBLED ,DON T MIND MUCH.
CHEERS
solamon said:Riemann hypothesis SKELETON OF PROOF in www.guideforex.webs.com[/URL][/QUOTE]
There is no such at that site.
The Riemann Zeta Function is a mathematical function that was introduced by Bernhard Riemann in the 19th century. It is defined as the infinite sum of the reciprocal of all positive integers raised to a given power (usually denoted by s). The Riemann Zeta Function is denoted by the Greek letter ζ and is represented by the formula ζ(s) = 1 + 1/2^s + 1/3^s + 1/4^s + ...
Complex zeros in the Riemann Zeta Function are values of s for which ζ(s) = 0. These zeros lie on the complex plane and have a real part of 1/2. The Riemann Hypothesis, one of the most famous unsolved problems in mathematics, states that all the non-trivial zeros of the Riemann Zeta Function lie on the line Re(s) = 1/2.
The complex zeros of the Riemann Zeta Function have connections to many areas of mathematics, including number theory, algebraic geometry, and physics. They also have implications in the distribution of prime numbers and the behavior of certain functions. Understanding the distribution of complex zeros can lead to a better understanding of the Riemann Zeta Function and other related functions.
No, it is not currently possible to find all the complex zeros of the Riemann Zeta Function. As mentioned before, the Riemann Hypothesis, which states that all the non-trivial zeros lie on the line Re(s) = 1/2, is still an unsolved problem. While we have found many zeros, it is believed that there are infinitely many more that have not yet been discovered.
The Riemann Zeta Function has a close connection to the prime counting function, which counts the number of prime numbers less than or equal to a given number. The distribution of complex zeros of the Riemann Zeta Function is related to the distribution of prime numbers, and the Riemann Hypothesis, if proven true, would give us a precise formula for the number of primes less than a given number. This connection is one of the reasons why the Riemann Hypothesis is considered one of the most important unsolved problems in mathematics.