Math Is Fun Forum

therussequilibrium

Member

Registered: 2012-12-21

Posts: 36

Golden Key - Riemann Zeta Function

Okay, I'm confused on something that's probably rather basic but it's really annoying me so a little help would be appreciated.

I'm reading a book and it's going over how the Golden Key was arrived at by basically using the Sieve of Eratosthenes on the Riemann Zeta Function.

And it gets to this point

ζ(s)=1+1/2s+1/3s+1/4s+....
Then you multiply both sides by the fist expression and subtract the new expression by the first expression and you end up hypothetically with something like:

...(1-1/7s)(1-1/5s)(1-1/3s)(1-1/2s)ζ(s)=1

Well here’s the part that just isn’t computing to me, it’s saying that the next step that was taken was dividing the left side by the right side, fair enough if it ended up being ζ(s)=1/(the entire term that was on the left).

Instead, it says that after dividing the left side by the right side we end up with:
ζ(s)=[(1)/1-1/2s))*((1)/(1-1/3s)]...

This makes absolutely no sense to me, and I tried working it out myself by doing this:
(1/2)(1/2)(1/2) = a; where a obviously is equal to 1/8

and if you divide how it shows to divide, you end up with:
1= (.125/.5)x(.125/.5)x(.125/.5)

And this obviously isn’t right, so could someone please explain how this was arrived at correctly?

Last edited by therussequilibrium (2013-01-08 00:42:59)

therussequilibrium

Member

Registered: 2012-12-21

Posts: 36

Re: Golden Key - Riemann Zeta Function

Nevermind lol, I have solved my ignorance on my own.

example:

(5)(5)(5)x=1
x=(1/5)*(1/5)*(1/5)

Man I'm retarded, sorry to waste anyone's time.

Last edited by therussequilibrium (2013-01-08 01:29:53)

therussequilibrium

Member

Registered: 2012-12-21

Posts: 36

Re: Golden Key - Riemann Zeta Function

I guess it just comes down to that the right side of the equation has to equal one before you can do this? I guess that's it...

noelevans

Member

Registered: 2012-07-20

Posts: 236

Re: Golden Key - Riemann Zeta Function

Hi therussequilibrium! 

You didn't waste my time.  I enjoyed looking up and reading about the Riemann Zeta function.
Quite interesting (and mostly over my head).  Gauss at age 15 came up with the n/ln(n) formula!
He was quite the genius, eh?

Have a blessed day!

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Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.