Eisenstein series identities based on partial fraction decomposition

2014/02/07 by Minoru Hirose, Hirose, Minoru, Nobuo Sato +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1402.1585

Abstract

From the theory of modular forms, there are exactly [(k-2)/6] linear relations among the Eisenstein series E_k and its products E_2iE_k-2i (2≤ i ≤ [k/4]). We present explicit formulas among these modular forms based on the partial fraction decomposition, and use them to determining a basis of the space of modular forms of weight k on \rm SL₂(\mathbb Z).

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