Friday, November 3, 2017 - 2:15pm
Trinity College Dublin and Georgia Institute of Technology
In this talk, I will summarize forthcoming work with Griﬃn, Ono, and Zagier. In 1927, P´olya proved that the Riemann Hypothesis is equivalent to the hy-perbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has been proved for degrees d ≤ 3. We obtain an arbitrary precision asymptotic formula for the derivatives Ξ(2n)(0), which allows us to prove the hyperbolicity of 100% of the Jensen polynomials of each degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This general condition also conﬁrms a conjecture of Chen, Jia, and Wang.