Very nice ...
@graveolens
in reply to @jamestanton
Show in a regular heptagon of side length 1 there are two diagonal of lengths a and b that satisfy 1/a + 1/b = 1.pic.twitter.com/Q2GMpDoInK
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I made this a few months ago: it doesn't amount to the demonstration you requested, but I can speak to the trees I am barking up here: The (ordinary) Fibonacci zeta function is known to have regularly spaced poles in a half plane (link to picture shortly)
Wendy Krieger produced this: http://os2fan2.com/p7flat.html and that would imply you get different sorts of zeta functions depending on the limit of some given slope (so, I guess you get zeta functions which are 'rational' and 'irrational'), and it's not known what the limits
are explicitly (in closed form or whatnot) Here is a link to Souichiro Ikebe's math functions site with complex phase portraits of the Fibonacci zeta function: http://math-functions-1.watson.jp/sub1_spec_030.html#section060 …
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