Comments on: The De Bruijn-Newman constant is non-negative
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoThu, 28 Feb 2019 13:30:32 +0000
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By: Dan Romik Studies the Riemann’s Zeta Function, and Other Zeta News. | Combinatorics and more
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-513264
Thu, 28 Feb 2019 13:30:32 +0000http://terrytao.wordpress.com/?p=10401#comment-513264[…] It is now the 10 year anniversary of polymath projects and let me belatedly mention a successful project polymath15 that took place over Terry Tao blog. The problem is related to the Hermite expansion of the Zeta function. Roughly speaking you can apply a noise operator on Zeta that causes higher degrees to decay exponentially. (The noise can be “negative” and then the higher degrees explode exponentially.) The higher the amount t of noise the easier the assertion of the Riemann Hypothesis (RH) becomes. Let , the de Bruijn-Newman constant, be the smallest amount of noise under which the assertion of RH is correct. It was conjectured that namely the assertion of the RH fails when you apply negative noise no matter how small. This follows from known conjectures on the spacing between zeroes of the Zeta function since when the assertion of RH is known for some level (positive or negative) of noise, then with a higher level of noise spacing between zeroes become more boring. The conjecture was settled by Brad Rodgers and Terry Tao. (See this blog post by Terry Tao.) […]
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By: Watching Over the Zeroes | Gödel's Lost Letter and P=NP
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-505898
Wed, 10 Oct 2018 17:55:30 +0000http://terrytao.wordpress.com/?p=10401#comment-505898[…] to a possible argument that the RH is false. In January of this year, Brad Rogers and Terence Tao turned up the heat on this connection by proving that the GUE conjecture entails the existence of […]
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By: Irfan Ali
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-503967
Wed, 15 Aug 2018 05:06:59 +0000http://terrytao.wordpress.com/?p=10401#comment-503967That’s a great move towards a Problem of Riemann I am student of MS Applied mathematics at IBA Sukkur University Sindh,Pakistan also working on the Problem but still iam reading the work which has done towards Riemann Hypothesis what would be the next move ?
working on constant is zero and see what happens either contradiction happens or not?
Or working in the region (0,0.22)?
Now which difficulties arises to work on the Newman constant is 0 or greater than 0?
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By: Heat flow and zeroes of polynomials II: zeroes on a circle | What's new
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-501372
Thu, 07 Jun 2018 11:15:46 +0000http://terrytao.wordpress.com/?p=10401#comment-501372[…] arguments in my paper with Brad Rodgers (discussed in this previous post) indicate that for a “typical” polynomial of degree that obeys the Riemann […]
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By: Polymath15, second thread: generalising the Riemann-Siegel approximate functional equation | What's new
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-492042
Sat, 03 Feb 2018 04:55:16 +0000http://terrytao.wordpress.com/?p=10401#comment-492042[…] real part on this strip. One can use the Poisson summation formula to verify that is even, (see this previous post for details). This lets us obtain a number of other formulae for . Most obviously, one can unfold […]
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By: Anonymous
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-491877
Mon, 29 Jan 2018 04:58:06 +0000http://terrytao.wordpress.com/?p=10401#comment-491877THE DE BRUIJN NEWMAN CONSTANT IS POSITIVE IF THE “FAMOUS” RIEMANN HYPOTHESIS IS WRONG. AS THE TITLE OF THIS BLOG POST SUGGESTS, COULD THIS BE A STEP TO DISPROVING THE RIEMANN HYPOTHESIS?
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By: Polymath15, first thread: computing $H_t$, asymptotics, and dynamics of zeroes | What's new
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-491837
Sun, 28 Jan 2018 00:10:41 +0000http://terrytao.wordpress.com/?p=10401#comment-491837[…] real part on this strip. One can use the Poisson summation formula to verify that is even, (see this previous post for details). This lets us obtain a number of other formulae for . Most obviously, one can unfold […]
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By: A new polymath proposal (related to the Riemann Hypothesis) over Tao’s blog | The polymath blog
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-491787
Fri, 26 Jan 2018 07:17:45 +0000http://terrytao.wordpress.com/?p=10401#comment-491787[…] Terry Tao’s blog who wrote: “Building on the interest expressed in the comments to this previous post, I am now formally proposing to initiate a “Polymath project” on the topic of obtaining new […]
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By: Terence Tao
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-491764
Thu, 25 Jan 2018 16:10:46 +0000http://terrytao.wordpress.com/?p=10401#comment-491764The literature so far has almost exclusively focused on implications of the form “information about zeroes of zeta” -> “information about the de Bruijn-Newman constant”, with the notable exception of course of the implication . It is conceivable that one could work on the converse and eventually show, for instance, that smallness of implies a zero free region for zeta which in turn implies some reasonably good error term in the prime number theorem. But given that our project to bound will use, among other things, numerical zero free regions for zeta and related functions, I would imagine that this would be an extremely inefficient route to get new information about zeta.
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By: El duro camino hacia la demostración de la hipótesis de Riemann | Ciencia | La Ciencia de la Mula Francis
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/#comment-491757
Thu, 25 Jan 2018 13:13:41 +0000http://terrytao.wordpress.com/?p=10401#comment-491757[…] matemáticos) en Terence Tao, “The De Bruijn-Newman constant is non-negative,” What’s new, 19 Jan 2018. Sabemos que 0 ≤ Λ < 1/2, reducir esta cota superior es el objetivo del nuevo proyecto […]
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