Factorizations of Eisenstein Series of Level up to 4

2021/03/13 by Henri Cohen, Cohen, Henri
Mathematics · #11F11 #11F37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2103.07698

openalex publication_date 2021/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the most standard Eisenstein series such as E₄(τ) or 2E₂(2τ)-E₂(τ), and also the function θ²(τ), are in a natural way the product of two conjugate Eisenstein series of half their weight and double their level, as well as a number of similar elementary identities for E₆ and Eisenstein series of levels 2, 3, and 4.

Related

• Identities about level 2 Eisenstein series
• Classical and adelic Eisenstein series
• Double zeta values, double Eisenstein series, and modular forms of level 2
• Eisenstein series identities based on partial fraction decomposition
• An Eisenstein series of rational weight