Economics Job Market Rumors Topic: A proof of the Riemann Hypothesis on the horizon.
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon
Economics Job Market Rumors Topic: A proof of the Riemann Hypothesis on the horizon.en-USSun, 25 Sep 2022 10:43:44 +0000http://bbpress.org/?v=1.0.2<![CDATA[Search]]>q
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Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8327560
Sun, 25 Sep 2022 08:34:46 +0000Economist8327560@https://www.econjobrumors.com/<blockquote><blockquote>
<blockquote>Algebraist here, so take this skeptically. Say we have a real analytic function on R^2 (or maybe {(x,y) with x>c} for some c). Say f decays reasonably quickly along vertical lines (like 1/|y|^(1+\epsilon), say). Then we can integrate along vertical strips to get a function on R. Is it again real analytic? I’m not seeing why it should be true.</p></blockquote>
<p>Maybe this isn't explicitly stated enough, but this question suggests an error in the paper.
</p></blockquote>
<p>Non-analyst here: According to <a href="https://math.stackexchange.com/questions/3495194/condition-for-integral-of-analytic-function-to-be-analytic" rel="nofollow">https://math.stackexchange.com/questions/3495194/condition-for-integral-of-analytic-function-to-be-analytic</a>, the footnote on page 4 at least holds for integrals of complex-analytic functions. I don't know if the argument can be adapted for real-analytic integrands, which is the case that the preprint requires.
</p></blockquote>
<p>Any real analytic function on some open subset of the real line can be extended to a complex analytic function on some open subset of the complex plane, so if the domain of the complex analytic extension is sufficiently big enough for what the author is trying to do that should be good enough. It looks like the author would basically get from integration by parts a sum of multiples of arctangents and arctangent anti-derivatives as the anti-derivative of the integrand.
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8327465
Sun, 25 Sep 2022 06:48:54 +0000Economist8327465@https://www.econjobrumors.com/<blockquote><p>Thinking of actually betting on this paper: <a href="https://manifold.markets" rel="nofollow">https://manifold.markets</a>
</p></blockquote>
<p>What are the odds ?
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8327229
Sun, 25 Sep 2022 03:51:23 +0000Economist8327229@https://www.econjobrumors.com/<blockquote><blockquote>Algebraist here, so take this skeptically. Say we have a real analytic function on R^2 (or maybe {(x,y) with x>c} for some c). Say f decays reasonably quickly along vertical lines (like 1/|y|^(1+\epsilon), say). Then we can integrate along vertical strips to get a function on R. Is it again real analytic? I’m not seeing why it should be true.</p></blockquote>
<p>Maybe this isn't explicitly stated enough, but this question suggests an error in the paper.
</p></blockquote>
<p>Non-analyst here: According to <a href="https://math.stackexchange.com/questions/3495194/condition-for-integral-of-analytic-function-to-be-analytic" rel="nofollow">https://math.stackexchange.com/questions/3495194/condition-for-integral-of-analytic-function-to-be-analytic</a>, the footnote on page 4 at least holds for integrals of complex-analytic functions. I don't know if the argument can be adapted for real-analytic integrands, which is the case that the preprint requires.
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8326903
Sun, 25 Sep 2022 00:55:30 +0000Economist8326903@https://www.econjobrumors.com/<blockquote><p>Algebraist here, so take this skeptically. Say we have a real analytic function on R^2 (or maybe {(x,y) with x>c} for some c). Say f decays reasonably quickly along vertical lines (like 1/|y|^(1+\epsilon), say). Then we can integrate along vertical strips to get a function on R. Is it again real analytic? I’m not seeing why it should be true.</p></blockquote>
<p>Maybe this isn't explicitly stated enough, but this question suggests an error in the paper.
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8326879
Sun, 25 Sep 2022 00:38:42 +0000Economist8326879@https://www.econjobrumors.com/<blockquote><p>Heard that this paper was discussed on the sidelines of the analytic number theory conference at the Universite de Montreal, held in celebration of Andrew Granville's birthday. Can someone in Montreal confirm this ?
</p></blockquote>
<p>Would love to know more about it.</p>
<p>I think the paper is a sincere effort. If it is incorrect, I would like to know where the errors are.
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8326809
Sun, 25 Sep 2022 00:08:40 +0000Economist8326809@https://www.econjobrumors.com/<p>Heard that this paper was discussed on the sidelines of the analytic number theory conference at the Universite de Montreal, held in celebration of Andrew Granville's birthday. Can someone in Montreal confirm this ?
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8325202
Sat, 24 Sep 2022 04:39:36 +0000Economist8325202@https://www.econjobrumors.com/<p>The linked post is a different setup and not relevant to what is considered in that preprint.</p>
<blockquote><blockquote>Algebraist here, so take this skeptically. Say we have a real analytic function on R^2 (or maybe {(x,y) with x>c} for some c). Say f decays reasonably quickly along vertical lines (like 1/|y|^(1+\epsilon), say). Then we can integrate along vertical strips to get a function on R. Is it again real analytic? I’m not seeing why it should be true.</p></blockquote>
<p><a href="https://math.stackexchange.com/questions/3783816/integral-of-an-analytic-function-also-analytic" rel="nofollow">https://math.stackexchange.com/questions/3783816/integral-of-an-analytic-function-also-analytic</a>
</p></blockquote>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8324620
Fri, 23 Sep 2022 21:53:54 +0000Economist8324620@https://www.econjobrumors.com/<p>Thinking of actually betting on this paper: <a href="https://manifold.markets" rel="nofollow">https://manifold.markets</a>
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8312106
Mon, 19 Sep 2022 09:29:05 +0000Economist8312106@https://www.econjobrumors.com/<p>Is it done bros?<br />
-An economist
</p>Economist on "A proof of the Riemann Hypothesis on the horizon."
https://www.econjobrumors.com/topic/a-proof-of-the-riemann-hypothesis-on-the-horizon/page/42#post-8312104
Mon, 19 Sep 2022 09:27:00 +0000Economist8312104@https://www.econjobrumors.com/<blockquote><p>Algebraist here, so take this skeptically. Say we have a real analytic function on R^2 (or maybe {(x,y) with x>c} for some c). Say f decays reasonably quickly along vertical lines (like 1/|y|^(1+\epsilon), say). Then we can integrate along vertical strips to get a function on R. Is it again real analytic? I’m not seeing why it should be true.</p></blockquote>
<p><a href="https://math.stackexchange.com/questions/3783816/integral-of-an-analytic-function-also-analytic" rel="nofollow">https://math.stackexchange.com/questions/3783816/integral-of-an-analytic-function-also-analytic</a>
</p>