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

Subject: Number Theory

Class: Scientific


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.