# Number Theory

## Polya’s Program for the Riemann Hypothesis and Related Problems

Speaker:
Ken Ono
Date:
Thu, Nov 9, 2017
Location:
PIMS, University of British Columbia
Conference:
PIMS-UBC Math Distinguished Colloquium
Abstract:

In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has only been proved for degrees d=1, 2, 3. We prove the hyperbolicity of 100% of the Jensen polynomials of every degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.

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