Math Colloquia

1707

Date | Apr 25, 2019 |
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Speaker | Kim, Henry |

Dept. | Univ. of Toronto / KIAS |

Room | 129-101 |

Time | 16:00-17:00 |

Unconditional results without an unproved hypothesis such as the generalized Riemann hypothesis (GRH) are very weak for an individual number field. But if we consider a family of number fields, one can prove just as strong results as we would assume GRH, in the form: (1) average result in the family; (2) the result is valid for almost all members except for a density zero set. We will explain this philosophy using examples of logarithmic derivatives of L-functions, residues of Dedekind zeta functions, and least primes in a conjugacy class.

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