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What does the Riemann zeta function have to do with the distribution of primes?

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Re: What does the Riemann zeta function have to do with the distribution of primes?

#31
post #24

Earlier quoted context omitted.

Is it not obvious? Replace “fairly despicable” with “white nationalist” instead of whatever anyone might imagine could make a mathematician despicable?

Why does this shorthand upset you?

I am not upset. It is obviously obstusely, impenetrably vague. What is your problem?

Re: What does the Riemann zeta function have to do with the distribution of primes?

#32
post #25
post #8

Although the author turned out to be a fairly despicable person, Prime Obsession is an absolutely wonderful book on this subject.

This is one of the few places I ever engage on the internet, but I think it may be time for HN to be read-only, too. This didn't seem especially controversial of a comment, and even here there's no end of the rotten attitudes for no good reason

What you call rotten attitudes seemed like fairly thoughtfully doing the research you left out of an opaque and off-topic character determination.

Read-only or read never is looking wiser than it did a few years ago.

Re: What does the Riemann zeta function have to do with the distribution of primes?

#33
Good article, but there is one step in the reasoning that rubs me the wrong way:

> This equation might seem a little hard to solve, but at this point you might notice something funny: $equation$

> So, if F′(x)log⁡(x)=1,F′(x)log(x)=1, then

> Thus, our mystery function F(x)F(x) obeys F′(x)log⁡(x)=1.F′(x)log(x)=1. From here you deduce F′(x)=1/log⁡(x),F′(x)=1/log(x), so by integrating you get

But it does not seems that F needs to have that trait, just that 1 works in that instance. It's sufficient but not necessary. How can you tell that it is that simple solution which is the right one?

Re: What does the Riemann zeta function have to do with the distribution of primes?

#35

Earlier quoted context omitted.

It doesn’t change if you apply it to complex arguments does it? Zeta(z) = 1 + 1/2^z + 1/3^z + … Where z in C. In fact, I thought that was why it’s called the Riemann zeta function. Euler applied it to an integer whereas Riemann applied it to complex arguments. Edit to add: my memory was correct. Reimann extended Euler’s definition to all complex s not equal to 1. https://en.wikipedia.org/wiki/On_the_Number_of_Primes_…

that definition only converges for Re(z)>1. for Re(z)<=1, you need alternate formulas

Yes. Riemann gives them in the paper, including derivation, it’s just a bit annoying to type/read them here because hn doesn’t support mathjaxx.

https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-...

Re: What does the Riemann zeta function have to do with the distribution of primes?

#36
post #24

Earlier quoted context omitted.

Is it not obvious? Replace “fairly despicable” with “white nationalist” instead of whatever anyone might imagine could make a mathematician despicable?

Why does this shorthand upset you?

A shorthand is generally unambiguous in context; this was not.

Re: What does the Riemann zeta function have to do with the distribution of primes?

#37

Earlier quoted context omitted.

I despise vague and quasi-anonymous attacks like this. "Trust me, online person, I, a random netizen, have made a moral judgment and you should have complete faith in it." Google summarizes the controversy thus, from Wikipedia: "John Derbyshire is an American journalist and political commentator. He was one of the last paleoconservatives at the National Review, until he was fired in 2012 for writing an article for Ta…

Would you prefer OC was more specific, ie “the author turned out to be a racist”, or do you have an issue with calling someone like this despicable?

Obviously, I would prefer OC was more specific. I said as much.

Re: What does the Riemann zeta function have to do with the distribution of primes?

#38

Earlier quoted context omitted.

that definition only converges for Re(z)>1. for Re(z)<=1, you need alternate formulas

Yes. Riemann gives them in the paper, including derivation, it’s just a bit annoying to type/read them here because hn doesn’t support mathjaxx. https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-...

I'm just not mathematician enough to convert that into a C function. Let alone one that is both efficient and reasonably accurate.

Re: What does the Riemann zeta function have to do with the distribution of primes?

#39

Earlier quoted context omitted.

Would you prefer OC was more specific, ie “the author turned out to be a racist”, or do you have an issue with calling someone like this despicable?

Obviously, I would prefer OC was more specific. I said as much.

Genuine question: are you on the spectrum? I find this reaction strange

Re: What does the Riemann zeta function have to do with the distribution of primes?

#40
post #36

Earlier quoted context omitted.

Why does this shorthand upset you?

A shorthand is generally unambiguous in context; this was not.

Why does it matter to you so much that OC is unambiguous?
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