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“This left a small but unsettling possibility that many zeros could be hiding out right at three-quarters.” Ok, but if zeros there are found some mathematician
by nyc111 2y ago
“This left a small but unsettling possibility that many zeros could be hiding out right at three-quarters.”
Ok, but if zeros there are found some mathematicians may as well call them “trivial zeros.” Can there be an objection to that?
- seanhunter 2y agoThis is way above my paygrade, but trivial zeros of the zeta function are at the negative even integers (ie they are of the form s = -2n for some natural number n) because that's what Riemann said in his paper where he made the conjecture[1] This equation now gives the value of the function ζ(s) for all complex numbers s and shows that this function is one-valued and finite for all finite values of s with the exception of 1, and also that it is zero if s is equal to a negative even integer. I don't think people get to retcon some other kind of zero into being trivial. [1] https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-translation.pdf https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-...