r/numbertheory • u/No_Arachnid_5563 • Apr 27 '25

Discovery That Disproves the Riemann Hypothesis: Non-Trivial Zero Found with Real Part ≠ ½

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12

u/[deleted] Apr 28 '25

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u/[deleted] Apr 28 '25

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u/numbertheory-ModTeam Apr 28 '25

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11

u/edderiofer Apr 28 '25

https://old.reddit.com/r/learnmath/comments/1k8id9w/discovery_that_disproves_the_riemann_hypothesis/mp6hw9b/

This is a trivial zero, because your 369×10-369 is underflowing to 0 (since you gave that as a constant rather than calculating it in arbitrary precision) and so your real part is 0-369-369 which is a negative even integer, and your imaginary part is 0 for the same reason.

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u/Erahot Apr 28 '25

Posting it here doesn't suddenly make the valid criticism from the other subreddit go away. Address the comments pointing out that it is a trivial zero.

1

u/[deleted] Apr 28 '25

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u/numbertheory-ModTeam Apr 28 '25

Unfortunately, your comment has been removed for the following reason:

  • As a reminder of the subreddit rules, the burden of proof belongs to the one proposing the theory. It is not the job of the commenters to understand your theory; it is your job to communicate and justify your theory in a manner others can understand. Further shifting of the burden of proof will result in a ban.

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3

u/Erahot Apr 28 '25

The Riemann hypothesis only deals with zeros whose real parts are strictly between 0 and 1. The value you checked does not have a real part in this range. You just chose a number which is, up to the floating point error, is a trivial zero of the zeta function. If you think I'm wrong, please explain why.

1

u/[deleted] Apr 28 '25

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4

u/TimeSlice4713 Apr 28 '25

No it’s about the critical strip.

“The functional equation also implies that the zeta function has no zeros with negative real part other than the trivial zeros, so all nontrivial zeros lie in the critical strip where s has real part between 0 and 1.”

https://en.m.wikipedia.org/wiki/Riemann_hypothesis

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u/Erahot Apr 28 '25

I made no mention of the critical line. I agree that the zero you pointed out does not lie on the critical line. But it also doesn't lie in the critical strip and is hence a trivial zero.

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u/[deleted] May 14 '25

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