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<p>We revisit the Ramanujan–Serre derivative map on the space of modular forms, give a re-interpretation as a differential operator on the space of quasimodular forms. We study various algebraic properties of the differential operator, give applications in the direction of the study of the Chazy equation, Niebur’s identity, van der Pol’s identity and evaluation of convolution sums of divisor functions.</p>

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A revisit to Ramanujan–Serre derivative map on quasimodular forms and some applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月19日

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  • Raveena Ganash,
  • Brundaban Sahu

摘要

We revisit the Ramanujan–Serre derivative map on the space of modular forms, give a re-interpretation as a differential operator on the space of quasimodular forms. We study various algebraic properties of the differential operator, give applications in the direction of the study of the Chazy equation, Niebur’s identity, van der Pol’s identity and evaluation of convolution sums of divisor functions.