By way of actual analysis, the proof relies heavily (entirely) on the properties of something called a Todd function. These are glossed over, but there appears to be some rigor in that prior work.
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The Todd function is claimed to have some properties that are relevant; namely, that it reduces to an (analytic) polynomial on compact sets, and that under its transformation certain sets “look” the same.
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The paper does bury some arguments, but this is not uncommon for something at this level. Perhaps the surprise is how much it leans on rather basic principles of complex analysis.
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Same. I'm leaning no, but it's more due to Atiyah's meanderings (e.g. in the fine structure paper) are a bit "obtuse" and either missing something fundamental regarding his Todd function... but it did (does) make me wonder.
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It’s clear that the Todd function does all ththe heavy lifting. And I would need to see some rigor on the arguments of compactness and that it collapses to a polynomial in compact sets. Weak analyticity seems like a property fraught with nuance.
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Where are the properties of the Riemann zeta function used beyond analyticity? I'm not seeing where this argument fails for other functions.
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Yeah. I’m giving the benefit of the doubt that some of that is buried in the Todd function prior work
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