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Much is made of the search for a proof of the Riemann hypothesis via the field with one element. Are there any lesser classic arithmetic results that have been proved with F_1 geometry, such as the prime number theorem? Do any such proofs seem within reach of current models of F_1 geometry?

Thanks in advance!

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  • $\begingroup$ I think the answer is a resounding no $\endgroup$
    – Daniel Loughran
    Commented Aug 13, 2023 at 9:20
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    $\begingroup$ Related: mathoverflow.net/questions/23394/… $\endgroup$
    – Daniel Loughran
    Commented Aug 13, 2023 at 9:22
  • $\begingroup$ Thanks for the link! I didn't know whether things had changed in the last ten or so years since that question... $\endgroup$
    – NZK
    Commented Aug 13, 2023 at 13:35

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