Joint IAS/Princeton University Number Theory Seminar

In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity had only been proved for degrees d=1,2,3. We prove the hyperbolicity of all (but possibly finitely many) the Jensen polynomials of every degree d. Moreover, we establish the outright hyperbolicity for all degrees d<10^26. These results follow from an unconditional proof of the "derivative aspect" GUE distribution for zeros. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.