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Date | Aug 29, 2023 |
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Speaker | 강민찬 |

Dept. | 서울대학교 |

Room | 129-301 |

Time | 13:30-15:00 |

The quantitative version of the Oppenheim conjecture, which was proved by Eskin, Margulis, and Mozes, states that for an indefinite quadratic form whose signature is neither (2,1) nor (2,2), and which is not proportional to a rational form, the values are asymptotically uniformly distributed. In the proof of the quantitative version of the Oppenheim conjecture, the alpha function is used essentially to control the value around the cusp. In this talk, we overview the usage of the alpha function, and primarily focus on the proof of the theorem which deals with the integration of the alpha function around the cusp on the space of unimodular lattices of the Euclidean space.

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