2022/11/22 by Arpit Das, Das, Arpit, Naveen Balaji Umasankar +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Identities #Coding theory and cryptography #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2211.15369
openalex publication_date 2022/11/22 · openalex created_date 2022/12/10 · openalex updated_date 2026/07/28
In this work we extend the study of arXiv:2210.07186 by investigating two- and three-character MLDEs for Fricke groups at prime levels. We have constructed these higher-character MLDEs by using a novel Serre-Ramanujan type derivative operator which maps k-forms to (k+2)-forms in Γ+0(p). We found that this novel derivative construction enabled us to write down a general prescription for obtaining Ramanujan-Eisenstein identities for these groups. We discovered several novel single-, two-, and three-character admissible solutions for Fricke groups at levels 2 and 3 after solving the MLDEs among which we have realized some in terms of Mckay-Thompson series and others in terms of modular forms of the corresponding Hecke groups. Among these solutions, we have identified interesting non-trivial bilinear identities. Furthermore, we could construct putative partition functions for these theories based on these bilinear pairings, which could have a range of lattice interpretations. We also present and discuss modular re-parameterization of MLDE and their solutions for Fricke groups of prime levels.