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The Pólya-Jensen criterion for the Riemann Hypothesis asserts that RH is equivalent to the hyperbolicity of certain Jensen polynomials for all degrees d ≥ 1 and all shifts n.

This criterion was used by GRIFFIN-ONO-ROLEN-ZAGIER in one of their recent paper: JENSEN POLYNOMIALS FOR THE RIEMANN ZETA FUNCTION AND OTHER SEQUENCES.

The original Pólya-Jensen criterion was published in German as:

G. Pólya, Über die algebraisch-funktionentheoretischen Untersuchungen von J. L. W. V. Jensen, Kgl. Danske Vid. Sel. Math.-Fys. Medd. 7 (1927), 3-33.

But I could not read German.

Where can we find a proof of the Pólya-Jensen criterion in English ? Does any other papers or text books or exposition also contain a proof ?

Thank you in advance.

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    $\begingroup$ See there for a proof of that criterion for the RH (with $f = (s^2+1/4) \Gamma(s/2) \pi^{-s/2} \zeta(s)$) $\endgroup$ – reuns Aug 19 at 20:42
  • $\begingroup$ Thank you. @reuns $\endgroup$ – david Aug 19 at 21:13

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