DMS Colloquium: Ken Ono

Speaker: Ken Ono, Asa Griggs Candler Professor of Mathematics (Emory University)

Title: Polya’s Program for the Riemann Hypothesis and Related Problems

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 all (but possibly finitely many) the Jensen polynomials of every degree \(d\). We obtain a general theorem which models such polynomials by Hermite polynomials, which in the case of the zeta-function can be thought of as a "degree aspect" GUE distribution. The general 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. 

Faculty host: Narendra Govil