Toric Modular Forms and Nonvanishing of L-functions
نویسنده
چکیده
In a previous paper [1], we defined the space of toric forms T (l), and showed that it is a finitely generated subring of the holomorphic modular forms of integral weight on the congruence group Γ1(l). In this article we prove the following theorem: modulo Eisenstein series, the weight two toric forms coincide exactly with the vector space generated by all cusp eigenforms f such that L(f, 1) 6= 0. The proof uses work of Merel, and involves an explicit computation of the intersection pairing on Manin symbols.
منابع مشابه
On Toric Varieties and Modular Forms
Let M∗(l) = M∗(Γ1(l),C) be the ring of holomorphic modular forms on Γ1(l). In this talk we use the combinatorics of complete toric varieties to construct a subring T∗(l) ⊂ M∗(l), the subring of toric modular forms (§2). This is a natural subring, in the sense that it behaves nicely with respect to natural operations on M∗(l) (namely, Hecke operators, Fricke involution, and the theory of oldform...
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