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SUMMARY:Qiao He (Columbia University)
DTSTART:20260428T190000Z
DTEND:20260428T200000Z
DTSTAMP:20260423T124647Z
UID:MITNT/136
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/136/">
 Functional Equations of Siegel-Weil Eisenstein Series</a>\nby Qiao He (Col
 umbia University) as part of MIT number theory seminar\n\nLecture held in 
 Room 4-231 at MIT (Building 4).\n\nAbstract\nFunctional equation of Eisens
 tein series is a fundamental and has many applications. The abstract formu
 lation involves intertwining operator\, and it is of great interest to mak
 e it explicit. In this talk\, we talk about an explicit functional equatio
 n of Siegel-Weil Eisenstein series associated to a quadratic/hermitian lat
 tice whose localization is a vertex lattice. Instead of using the definiti
 on of the intertwining operator to do the calculation directly\, we regard
  the Intertwining operator as a degenerate Whittaker function\, and make u
 se of the relation between Whittaker function and local density to inducti
 vely compute the formula. Even for the self-dual lattice case\, our method
  is new compared with the classical Gindikin-Karpovich method. As a result
 \, we obtain an elegant functional equation for the corresponding local de
 nsity polynomials too. This talk is based on a joint work with Chao Li\, Y
 ousheng Shi\, Tonghai Yang and Baiqing Zhu.\n
LOCATION:https://researchseminars.org/talk/MITNT/136/
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