A
function is a like a little computer. You feed
it a number. It calculates away using some set
programme and then outputs an answer.
What is the function or
programme that Riemann used:
Here is the formula for
what the computer does to x. It is called the
zeta function:
z (x)= 1/1x
+ 1/2x + 1/3x + …+
1/nx +…
It is like a cooking recipe.
This formula is like the cake, but how do you
cook the cake: Here are the three steps to cooking
Riemann’s zeta cake:
(1) Calculate 1x, 2x, 3x,
4x,… an infinite list of exponentials
[click
here to find out how to raise 4 to the power of
an imaginary number]
(2) Take the reciprocal of all the numbers in
step (1), i.e. calculate 1/nx.
(3) Add up all the numbers from step (2). [click
here to find out about adding up infinitely many
numbers]
Why
does this function have anything to do with primes?
Press here to find out.
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