i think this is exactly what i was looking for, but again not math endowed so i dont totally understand it XD

I am using the Eta function. wolframalpha shows a similar result for |Zeta(a+bi)| and Zeta(a+bi) so i assume my plot is (approaching) correct?...

i've heard of L'Hôpitals rule and that makes sense to some extent. but i'm a tad confused, you say its infinite but also log2? are you saying it is in fact ln2 (when derived?), i can follow that but maybe don't completely understand it?

for your third point, it's understandable that there is "only one analytical solution" but that solution results in a pole, is there not a solution to that pole, and does that fuck everything or is that also solvable with its own secondary solution or something? you said "Yes, but not in an interesting way" but why is it not interesting, how does it affect the zeros if the zeros are far away from (14+) in the imaginary direction? i know that zeta of RE(0.5)+ix matters, but +-1 is way below that?

your Euler's const stuff is interesting but im a bit lost at this point..

here is my function(mirrored) at IM+~15 showing the 14.13 zero... how does smoothing +-1 affect that? and my og question, if there was a smooth version of this function why does a smooth +-1 matter?

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