Complex Zeros in Riemann Zeta Function: Is it Possible?

[TheOogy]

in the Riemann Zeta function, is it possible to have two complex zeros off the critical strip that both have the same imaginary part?

 

[solamon]

you re asking a question that closes the problem of Riemann hypothesis , i see there s no answer for your question yet .Think about it again or reformulate ,or i m just lost with the question

 

[epkid08]

in the Riemann Zeta function, is it possible to have two complex zeros off the critical strip that both have the same imaginary part?

That have a different real part? I would think so. For instance, take s=1/4 and s=3/4 and plug them into the functional equation.
$$\zeta(s) = 2^s\pi^{s-1}\sin\left(\frac{\pi s}{2}\right)\Gamma(1-s)\zeta(1-s) \!$$

 

[TheOogy]

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]

i m wondering too why 1/4 and 3/4 ,i m wondering about p/2^n while p<2^n so that we stay in [0 1] with p prime.
i just have noticed the 3/4 , 5/4 when i considered if zeta(z) is close to o then instead of considering zeta(z) i plug in zeta(z) i mean zeta{(zeta(z)} and do some crafting just like heaviside has done on distribution ,some approximation and see the expression not for z but for the complex zeta(z) ...there might be something arround go on try if you have time .

 

[epkid08]

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.

I was implying that there probably exists a real number t (due to what I mentioned in my first post) which satisfies:

$$\Im[\zeta(1/4 + it)] = \Im [\zeta(3/4 + it)]= 0$$

etc. for other values of re(s)

 

[solamon]

have you got some proof,or it s not a statement?did you do some calclations?we can work only on proofs ,and close quickly debates because it s mathematics.

 

[TheOogy]

i don't have a proof, which is way I'm asking, i thought maybe someone can prove that there cannot be a pair with the same imaginary part but this turns out more complicated then i thought it would be.

 

[solamon]

oh yes i see .you can have an intuition that is true too .you might have a suitable answer .the information i got is that there are solutions with imaginary same absolute value .or with imaginary opposite. check $$\bar{z}$$ when z is a zero .I would like to make sure of your intuition ,but busy temporaly .later .cheers.

 

[TheOogy]

conjugates don't have the same imaginary part.

 

[solamon]

yes conjugates don t have have same imaginary except reals .
So try to find out about your idea ,have you some was ?

 

[rscosa]

Hi!
fortunately all the complex zeros outside of the known strip are negative and even integers, so of course all of them are (complex but real) zeros of the RZF and have the same imaginary part (equal to zero). But the RZF has no zeros with nonzero imaginary part outside of the strip $0<\re z<1$. By the way those zeros are called trivial zeros.

 

[solamon]

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 .

 

[CRGreathouse]

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 .

The RH is that there are no nontrivial zeros off the critical *line*. It has been proven that there are no nontrivial zeros off the critical *strip*.

 

[rscosa]

Hi!,
there is NOT an official proof but many people is trying hard.

 

[solamon]

Rh is very likely to be true . I have verified myself that if it s true there is not a problem still ,on the limit calculations theory .if it s false there is a big problem.
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.

 

[CRGreathouse]

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.

No one on this thread has said that there are no nontrivial zeros off the critical line. *I* said that there are no nontrivial zeros off the critical strip -- this is well-known.

 

[solamon]

yes it s easy to prove there are no non trivial zero off the crtical strip .cool then .
so .who knows if zeta can be real off the critical line but on the critical strip?then he s got a proof as well it looks .tell me something quickly where do you know zeta real ,for a variable complex on the critical strip with imaginary part different of zero.

 

[CRGreathouse]

so .who knows if zeta can be real off the critical line but on the critical strip?

Are you asking if anyone's solved the Riemann hypothesis?

 

[solamon]

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]

Riemann hypothesis SKELETON OF PROOF in www.guideforex.webs.com[/URL]

 

[HallsofIvy]

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

Are you trying to SAY something here?

Riemann hypothesis SKELETON OF PROOF in www.guideforex.webs.com[/URL][/QUOTE]
There is no such at that site.

 

[solamon]

in mathematics ressources of www.guideforex.webs.com[/URL] , and learn at the same time forex to profit from your math skills .

 

[Santa1]

All I can say is, What?!

 

[matticus]

if I'm not mistaken, i believe solamon is saying (in very broken english) that if you buy whatever product that website is selling you too can prove RH...

 

[solamon]

come visit www.guideforex.webs.com[/url] , Riemann hypothesis made easy ,and for any question just type it , there is a math editor .Rieman hypothesis demystified .Yes an easy proof in process there follow the update of the page [PLAIN]www.guideforex.webs.com on math page .

 

[Santa1]

Are you saying you have proved RH, and in an easy manner?

That website is some sort of commercial site?

I don't get you, or what that site has to do with number theory.

 

[solamon]

There is a commercial aspect of the website ,but in general it s my daily life ,the website .I have decided at the moment to make the website general :all in one website , even in physics page there is some cosmology :easy explanation or model of origin of universe from nothing , from 0 into x-x=o x has given universe -x the supernatural corpse or part of universe !
i have made in math page clear and easy explanation that Riemann hypothesis is true if there is no zero for real part>1/2 even on the crticial strip if real part <1/2 and if there is no there then the hypothesis is true
and have showed too that Riemann should just replace 1/2 + it by 1/2 -s or s-1/2 and show that $$\xi$$(1/2-s) has no zero on the critical strip , it s easier to prove that an equation has no zero than it s got particular zeros we can t list
and we can rewrite 1/2 - s en term of 1/2 -a -it and prove that $$\xi$$(1/2-a -it) has any real zero for any t ,with 0<a<1 . I don t have the time to type something ,but if you re interested to get some guidelines there are updated infos for an easy proof of Rh without lot of calculations . www.guideforex.webs.com[/URL]
because if $$\xi$$(1/2-a -it) has no zero at all for any t so does $$\zeta$$(1/2 - s) then it s clear that zeta s got non-trivial solution on the critical line only .
The reason of the website is putting math into work too so any mathematician could visit and get a career on the go , because i think , fundamental mathematics can t pay bills in the 21 th century ! so visit [PLAIN]www.guideforex.webs.com[/URL] , do mathematics and have a career too ,it means you ll do really mathematics because you do it because you love it .
if you hve any other question write me from the website , i m not very permanent here .

 

[Santa1]

I do not understand what you are saying about (edit:) "xi". Try to use more mathematical notation, it is a language we should both be able to understand.

I'm not sure I agree on how you "explain" the origins of the universe, but then again I'm not sure we agree on how your proof of RH is built up.

Please use mathematical notation or write very basic english.

 

[solamon]

ok Mr < D > , i write french better , but this forum is in english .
yes you re not sure wether the approach proves or not Rh .so
keep coming to the math page of the website ,that s all i can say .
agree that if zeta(1/2-s) has no zero for s on the crtical strip and if zeta(s-1/2) has no zero on the critical strip then non trivial zeros are on the critical line .If it s not clear tell me to explain more .

 

[Santa1]

Your math page requires a password and username, I am very skeptical as to joining a commercial site, especially if I'm unsure of the content.

When you say zeta(s-1/2) on the critical strip, do you mean when 1 > re s > 0 or when 1 > s-1/2 > 0 ?

Also if you show that zeta(s) is a zero in the critical strip, then you've already shown that zeta(1-s) is one.

If your proof is so simple, you should write it here.

 

[TheOogy]

solamon please, and I'm not saying it because I'm bad, and i don't want to hurt anyone, but please- SHUT UP!

p.s. please lock this thread.