Toric modular forms and nonvanishing of L-functions

Lev Borisov, Paul E. Gunnells

Research output: Contribution to journalArticle

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Abstract

In a previous paper [1], 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 languageEnglish (US)
Pages (from-to)149-165
Number of pages17
JournalJournal fur die Reine und Angewandte Mathematik
Issue number539
StatePublished - Dec 1 2001
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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