Section 25.5 Connecting to Zeta
Subsection 25.5.1 Turning the golden key
Now, this looks just as hopeless as before. How is
Subsection 25.5.2 Detailing the connections
Now let's connectThis reminds me of the old joke about Noah's ark and logarithms. So, after the ark lands, all the animals are … having baby animals, let's say. Except the snakes. No baby snakes. Noah asks what the problem is – they seem to be missing the point. Snakes say, no worries, just give us a wooden bench or sawhorse or something. Noah wonders what's up, but gives it to them. Next morning, tons of baby snakes! Naturally Noah has to ask where the magic was. “Simple; adders need a log table to multiply.”
Question 25.5.2.
What can we do with
Solution.
We can use its Taylor series!
\begin{equation*}
-\log(1-x)=\sum_{k=1}^\infty \frac{x^k}{k}
\end{equation*}
-
Whenever
reaches the sum of all those functions would add Adding up all of these for all means the total function would include -
Whenever
reaches the sum of all those functions would add This, however, is the same thing as when hits a prime, so we can add it to the previous point. The total function would include would include -
When
reaches a cube of a prime, the sum adds This is the same thing as adding a new part when hits a prime, that is adding