Back to Search
Start Over
Jensen polynomials for the Riemann zeta function and other sequences.
- Source :
-
Proceedings of the National Academy of Sciences of the United States of America . 6/4/2019, Vol. 116 Issue 23, p11103-11110. 8p. - Publication Year :
- 2019
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00278424
- Volume :
- 116
- Issue :
- 23
- Database :
- Academic Search Index
- Journal :
- Proceedings of the National Academy of Sciences of the United States of America
- Publication Type :
- Academic Journal
- Accession number :
- 136851568
- Full Text :
- https://doi.org/10.1073/pnas.1902572116