Differential Equations Satisfied by Modular Forms and K3 Surfaces
نویسندگان
چکیده
We study differential equations satisfied by modular forms of two variables associated to Γ1×Γ2, where Γi (i = 1, 2) are genus zero subgroups of SL2(R) commensurable with SL2(Z), e.g., Γ0(N) or Γ0(N)∗ for some N . In some examples, these differential equations are realized as the Picard–Fuchs differential equations of families of K3 surfaces with large Picard numbers, e.g., 19, 18, 17, 16. Our method rediscovers some of the Lian–Yau examples of “modular relations” involving power series solutions to the second and the third order differential equations of Fuchsian type in [14, 15].
منابع مشابه
Differential Equations Satisfied by Bi-modular Forms and K3 Surfaces
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