Lecture Preview: Twisted Siegel–Weil formulas for GL_2 over non-Galois quartic CM fields
Publication Time:2026-04-02
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Title
Twisted Siegel–Weil formulas for GL_2 over non-Galois quartic CM fields
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Time
March 24, 14:00
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Place
Room 4108, Mathematics Building
Abstract
Siegel–Weil formulas establish a relation between integrals of theta functions and Eisenstein series.
In this talk, we will introduce a twisted Siegel–Weil formula over non-Galois quartic CM fields, which shows that the twisted theta integral against a quadratic character is equal to the Doi–Naganuma lift of Hecke’s integral.
This implies that the base change of the Jacquet–Langlands correspondence for certain Hecke characters from ℚ to real quadratic fields by the Doi–Naganuma lift is surjective.
If time permits, we will also introduce its application to the computation of twisted CM values of Borcherds forms.
About the Speaker
Zhang Mingkuan is a postdoctoral researcher at the Technical University of Darmstadt. He obtained his Ph.D. from Harbin Institute of Technology in 2025. His research interests include Hilbert modular forms, theta lifts, and CM values of modular functions. His work has been published in journals such as Journal of Number Theory and International Journal of Number Theory.
