Modular forms and almost linear dependence of graded dimensions

2006/09/11 by Antun Milas, Milas, Antun
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT) #Quantum Algebra (math.QA) #math.NT #math.QA

paper · pdf · doi:10.48550/arxiv.math/0609308

Presented at the conference "Lie Algebras, Vertex Operator Algebras and Their Applications" NCSU, May 2005

arxiv created 2006/09/11 · openalex publication_date 2006/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every positive integral level k we study arithmetic properties of certain holomorphic modular forms associated to modular invariant spaces spanned by graded dimensions of L_sl₂(k Λ₀)-modules. We found a necessary and sufficient condition for their vanishing and showed that these modular forms resemble classical Eisenstein series E_2k+2(τ). Furthermore, we derived similar results for M(p,p') Virasoro minimal models, thus generalizing some results of Mortenson, Ono and the author.

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