Toric modular forms and nonvanishing of L-functions

Lev A. Borisov, Paul E. Gunnells

Research output: Contribution to journalArticlepeer-review

Abstract

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 G1.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 ; 1.30. 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
Volume2001
Issue number539
DOIs
StatePublished - Sep 20 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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