It's said that one of the first things that was done with a digital computer was computing the values of the zeroes of the zeta function, and that today it's known that the first gorrilion zeroes lie EXACTLY on the line.My question is, how can they "compute" something like that. They don't say that the zeroes lie arbitrarily close to the line, they say "exactly on the line". How is this possible, wouldn't you need a proof for something like that?
>>16775047Small brain here:Doesn't the fact that it's a zero mean it lies EXACTLY on the line by definition?
>>16775047>>16775051One the that finite state machine suck at is infinite precision maths. Anyone saying a computer calculated anything EXACTLY is a crack smoking monkey.Nothing about the Zeta function has been proven. We're not even sure that Zeta is its real name.
>>16775051>Doesn't the fact that it's a zero mean it lies EXACTLY on the line by definition?No...? z is a zero if and only if Zeta(z) = 0
>>16775059So it's zero. Therefore on the line.
>>16775068 There is an infinite amount of trivial zeroes on the x axis since zeta function descomposes as a product in which one of its factors is a trigonometric function. The line we are talking about is Re(z)=1/2. The problem is about the non trivial ones
>>16775057>Not Sure if zeta is its real namePop sci consumer, do not speak about scientific topics. We know you feel clever doing that but you are making a fool out of yourself.The concept was given the Name zeta Function, so it is the zeta Function.
>>16777895>Pop sci consumerI dare you to show me one popsci source that has ever called into question the naming of the Riemann Zeta fuction.
>>16777931There probably is none.
>>16777935I accept your apology.
>>16777959Why do you question a name?
>>16777987Is that not rule one of science? Question your assumptions and demand evidence?One popsci article questioning the name is enough to refute the unsubstantiated claim.
>>16775057>We're not even sure that Zeta is its real name.You are a disgusting subhuman retard, don't ever post in my thread again
>>16778580Your thread will slide into the abyss.I will still be here, with your uncertain certainty.
>>16775047I wish someone actually answered this.
>>16778910Be the change you want to see, Anon.
>>16778910By multiplying the Zeta function with the correct factors, you get the Xi function. The Xi function has the same zeros within the critical strip, but unlike the Zeta function it is purely real on the critical line. This means that you can find zeros on the line just by looking for sign changes of the Xi function.To confirm that you haven't missed any zeros (either on or to the side of the critical line) you can use the argument principle and integrate in a box-shaped contour. The result will be the number of zeros within the box (an integer).Neither of these steps needs an exact evaluation of the Zeta function, you can use a combination of ball arithmetic and approximations with provable error bounds to confirm the sign changes and calculate the integral.Of course, in truth the algorithms are a lot more advanced and efficient than this simple outline.
>>16779041Ok but this just seems like a proof of the Riemann Hypothesis? So they can count how many zero are in a given region and then prove they are all on the line? Why can't you generalize this to the entire strip?
