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Philadelphia Area Number Theory Seminar

Friday, November 3, 2017 - 2:15pm

Larry Rolen

Trinity College Dublin and Georgia Institute of Technology


Bryn Mawr College

Park Science Building, Room 328

Talk scheduled to begin at 2:40 PM. Tea and refreshments at 2:20 PM in Park Science Building, Room 339. Please note talk will take place on a Friday instead of the usual Wednesday.

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.