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Eisenstein series identities based on partial fraction decomposition

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Abstract

From the theory of modular forms, we know that 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 determine a basis for the space of modular forms of weight \(k\) on \(\mathrm{SL}_2 ({\mathbb Z})\).

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Authors and Affiliations

  1. Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan

    Minoru Hirose & Nobuo Sato

  2. 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Koji Tasaka

Authors
  1. Minoru Hirose
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  2. Nobuo Sato
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  3. Koji Tasaka
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Correspondence to Koji Tasaka.

Additional information

This work is partially supported by Japan Society for the Promotion of Science, Grant-in-Aid for JSPS Fellows (No. 231733, No. 241440, No. 257323).

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Hirose, M., Sato, N. & Tasaka, K. Eisenstein series identities based on partial fraction decomposition. Ramanujan J 38, 455–463 (2015). https://doi.org/10.1007/s11139-014-9639-7

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  • DOI: https://doi.org/10.1007/s11139-014-9639-7

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