Toric modular forms and nonvanishing of L-functions

Lev A. Borisov; Paul E. Gunnells

doi:10.1515/crll.2001.071

Toric modular forms and nonvanishing of L-functions

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	149-165
Number of pages	17
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2001
Issue number	539
DOIs	https://doi.org/10.1515/crll.2001.071
State	Published - Sep 20 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1515/crll.2001.071

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AU - Gunnells, Paul E.

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Toric modular forms and nonvanishing of L-functions

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