Monday, July 22, 2019

Oscillates

Been reading a current take on Riemann's paper
from a German university prof. Found a simpler statement
of the zeta function, which I am using to better understand
our working formula.

It is clear that the initial fraction - in a convergent expression -
is the signature of the complex plane. No matter what value
Re_s takes, we end up with a negative decimal on the bottom,
and a modest multiplier for the whole. The s as an exponent for n
serves to keep the (-1) term oscillating.




                                                         *     *     *

Been also wondering why, when one differentiates, constants disappear
to zero when, if we take them as ln values, we end up with a fraction.
Turns out there is a whole branch of mathematics for that, Fractional
Calculus, and field equations in physics use this. I mention it because,
at the time of Riemann's paper, physics and mathematics were one. And
he does make reference to Fourier analysis...



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