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# Jensen polynomials for the Riemann zeta function and other sequences

Edited by Kenneth A. Ribet, University of California, Berkeley, CA, and approved April 8, 2019 (received for review February 12, 2019)

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## Significance

The Pólya–Jensen criterion for the Riemann hypothesis asserts that

## Abstract

In 1927, Pólya proved that the Riemann hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. Email: ken.ono{at}emory.edu.

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2017.

Author contributions: M.G., K.O., L.R., and D.Z. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

See Commentary on page 11085.

- Copyright © 2019 the Author(s). Published by PNAS.

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

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