Gross–Zagier reading seminar: Modular Forms and Hecke Operators
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چکیده
Our goal is to give an introduction to modular forms and to discuss the role of Hecke operators in the theory. We will focus on the parts of the theory that we will need in studying [GZ86]. For more details, one can refer to [DI95]. Recall the following topics from Jeff’s talks: • The Atkin-Lehner involution Wk is an involution on the modular curve Y0(N) = h/Γ0(N) and permute the cusps. • Eisenstein series... • A Heegner point is a point in the modular curve Y0(N) = h/Γ0(N) corresponding to N -isogenous elliptic curves E,E′ with CM by the same order O.
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