Tuesday, December 17 2019

15:30 - 16:20

15:30 - 16:20

* Venue | Media Centre |

* Speaker | Larry Rolen |

* Title | Jensen-Polya Criterion for the Riemann Hypothesis and Related Problems |

Affiliation | Vanderbilt University |

Abstract | In the first talk, I will summarize forthcoming work with Griffin, Ono, and Zagier. In 1927 Pólya 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. |

* Announcement? | Institute |

* Refreshments? | Before the event |

* Honorarium? | None |

Special Arrangements? | None |

* Host name and email |

Done