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arXiv · 1402.1585

Eisenstein series identities based on partial fraction decomposition

Minoru Hirose·Nobuo Sato·Koji Tasaka
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Abstract

From the theory of modular forms, there are exactly $[(k-2)/6]$ linear relations among the Eisenstein series $E_k$ and its products $E_{2i}E_{k-2i}\ (2\le i \le [k/4])$. 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 ${\rm SL}_2({\mathbb Z})$.

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Minoru Hirose, Nobuo Sato, Koji Tasaka. 2014-02-07. Eisenstein series identities based on partial fraction decomposition. https://arxiv.org/abs/1402.1585

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