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Does anyone know who formulated this conjecture related to Riemann's zeta function?

Conjecture. The set $$\{ x : \exists y \space \space \zeta (x+iy) = 0\}$$ is dense in $[0, 1]$.

In other words the conjecture states that the real parts of the nontrivial Zeta zeros are dense in [0, 1]. Some time ago I read about this conjecture in a review paper about Riemann's Zeta function but I cannot remember the name of the author. Other details/references appreciated.

YCor
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Cristian Dumitrescu
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  • I wonder which piece of evidence can support such a conjecture... – Sylvain JULIEN Oct 25 '20 at 21:48
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    Weird. The more usual conjecture is that it consists of just one point. – Todd Trimble Oct 25 '20 at 21:50
  • I know , it's shocking and completely opposite to Riemann's Hypothesis but I guarantee the conjecture exists. I just can't remember who formulated it. I would also be interested in any other details/references related to it. – Cristian Dumitrescu Oct 25 '20 at 21:56
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    I suspect it was not so much a conjecture as a way to show just how far away we are from a proof of the Riemann Hypothesis. There is a thread somewhere here on MathOverflow about "outrageous conjectures" like this. Found the thread: https://mathoverflow.net/questions/259844/the-most-outrageous-or-ridiculous-conjectures-in-mathematics – Gerry Myerson Oct 25 '20 at 22:27
  • I accept your point of view but I cannot speculate on the intent of the author that formulated this statement. I just want to remember his name and find any relevant references that mention his conjecture. – Cristian Dumitrescu Oct 25 '20 at 23:26
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    In the absence of any details about the author, it might help to avoid male pronouns. –  Oct 26 '20 at 01:02
  • In the same spirit: The Alternative Hypothesis concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between nontrivial zeros is supposed to always lie at a half integer. – Carlo Beenakker Oct 26 '20 at 15:38

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