25th October: Siqi Yang

Title: Introduction to classical Hilbert modular forms

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Abstract: Hilbert modular forms are generalizations of modular forms from Q to totally real number fields F. In this talk, we will first recall classical modular forms and then introduce the classical Hilbert modular forms. Some properties of modular forms have analogues in Hilbert modular forms, but there are also interesting differences. One of the interesting properties of Hilbert modular forms is Koecher's Principle, which tells us that when F≠Q, each weak holomorphic Hilbert modular form is automatically holomorphic at cusps, and if furthermore the weight k is not parallel, it must be a cuspform.