It's a bit surprising that even on the so-called 'critical line' where s = ½ + ix for x real, the Riemann zeta function ζ(𝑠) looks a lot like the much simpler function
1/(1 - 2⁻ˢ)(1 - 3⁻ˢ...
Even if we go up to 1000 ≤ x ≤ 1100, we see the simple function
1/(1 - 2⁻ˢ)(1 - 3⁻ˢ)(1 - 5⁻ˢ) (where s = ½ + ix )
making a noble attempt to mimic the biggest peaks in the Riemann zeta function! By now there are places where it doesn't quite manage the job. But still, they look a bit alike.
(2/n)
1/(1 - 2⁻ˢ)(1 - 3⁻ˢ)(1 - 5⁻ˢ) (where s = ½ + ix )
making a noble attempt to mimic the biggest peaks in the Riemann zeta function! By now there are places where it doesn't quite manage the job. But still, they look a bit alike.
(2/n)
1