In a previous paper , we defined the space of toric forms script T sign(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) ≠ 0. The proof uses work of Merel, and involves an explicit computation of the intersection pairing on Manin symbols.
|Original language||English (US)|
|Number of pages||17|
|Journal||Journal fur die Reine und Angewandte Mathematik|
|State||Published - Dec 1 2001|
All Science Journal Classification (ASJC) codes
- Applied Mathematics