MathCS Seminar

Title: Jensen-Polya Criterion for the Riemann Hypothesis and Related Problems
Seminar: Algebra
Speaker: Larry Rolen of Trinity College Dublin and Georgia Tech
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-10-17 at 4:00PM
Venue: W306
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Abstract:
In this talk, I will summarize forthcoming work with Griffin, Ono, and Zagier. In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann's Xi-function. This hyperbolicity has been proved for degrees $d\leq3$. We obtain an arbitrary precision asymptotic formula for the derivatives $\Xi^{(2n)}(0)$, 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.

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