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<p>Using the Rankin–Selberg method with Poincaré series, we establish some formulas about Rankin–Cohen brackets of Hecke eigenforms and shifted convolution series of half-integral weight modular forms. For example, we show that this gives some non-trivial relations about Fourier coefficients of Hecke eigenforms and shifted convolution series. This generalizes a result of Choie, Kohnen and Zhang on Rankin–Cohen brackets of Hecke eigenforms of level one.</p>

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Rankin–Cohen brackets of Hecke eigenforms and shifted convolution series

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Wei Wang

摘要

Using the Rankin–Selberg method with Poincaré series, we establish some formulas about Rankin–Cohen brackets of Hecke eigenforms and shifted convolution series of half-integral weight modular forms. For example, we show that this gives some non-trivial relations about Fourier coefficients of Hecke eigenforms and shifted convolution series. This generalizes a result of Choie, Kohnen and Zhang on Rankin–Cohen brackets of Hecke eigenforms of level one.