On differential equations satisfied by modular forms
نویسندگان
چکیده
منابع مشابه
Differential Equations Satisfied by Modular Forms and K3 Surfaces
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 ...
متن کاملDifferential Equations Satisfied by Bi-modular Forms and K3 Surfaces
We study differential equations satisfied by bi-modular forms associated to genus zero subgroups of SL2(R) of the form Γ0(N) or Γ0(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” involv...
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A unified treatment is given of low-weight modular forms on Γ0(N), N = 2, 3, 4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, from which a single nonlinear third-order equation, called a generalized Chazy equation, can be derived. As byproducts of this result, a table of divisor function...
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We consider a class of linear ordinary differential equations determined by a modular form of weight one, and construct vector-valued modular forms of weight two by using solutions of such differential equations.
متن کاملDifferential operators on Hilbert modular forms
We investigate differential operators and their compatibility with subgroups of SL2(R) n. In particular, we construct Rankin–Cohen brackets for Hilbert modular forms, and more generally, multilinear differential operators on the space of Hilbert modular forms. As an application, we explicitly determine the Rankin– Cohen bracket of a Hilbert–Eisenstein series and an arbitrary Hilbert modular for...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2004
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-003-0573-4