Mathematicians Revive Abandoned Approach to the Riemann Hypothesis

[jedishrfu]

TL;DR

Many ways to approach the Riemann Hypothesis have been proposed during the past 150 years, but none of them have led to conquering the most famous open problem in mathematics. A new paper in the Proceedings of the National Academy of Sciences (PNAS) suggests that one of these old approaches is more practical than previously realized.

https://phys.org/news/2019-05-mathematicians-revive-abandoned-approach-riemann.html
and more on the Reimann Hypothesis backstory from Numberphile:

 

[TeethWhitener]

Link to (possibly paywalled) paper:
https://www.pnas.org/content/early/2019/05/20/1902572116

(Temporary) citation:
Jensen polynomials for the Riemann zeta function and other sequences
Michael Griffin, Ken Ono, Larry Rolen, and Don Zagier
PNAS first published May 21, 2019 https://doi.org/10.1073/pnas.1902572116

Abstract:
In 1927, Pólya proved that the Riemann hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function ζ(s) at its point of symmetry. This hyperbolicity has been proved for degrees d≤3. We obtain an asymptotic formula for the central derivatives ζ(2n)(1/2) that is accurate to all orders, which allows us to prove the hyperbolicity of all but finitely many of the Jensen polynomials of each degree. Moreover, we establish hyperbolicity for all d≤8. These results follow from a general theorem which models such polynomials by Hermite polynomials. In the case of the Riemann zeta function, this proves the Gaussian unitary ensemble random matrix model prediction in derivative aspect. The general theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function.

 

[Klystron]

Link to (possibly paywalled) paper:
https://www.pnas.org/content/early/2019/05/20/1902572116

(Temporary) citation:
Jensen polynomials for the Riemann zeta function and other sequences
Michael Griffin, Ken Ono, Larry Rolen, and Don Zagier
PNAS first published May 21, 2019 https://doi.org/10.1073/pnas.1902572116

Abstract:
In 1927, Pólya proved that the Riemann hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function ζ(s) at its point of symmetry...

FTR I am able to read the article using Mozilla Firefox w/o pay request. Thanks for the reference.