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Eigenform product identities for Hilbert modular forms

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We prove that amongst all real quadratic fields and all spaces of Hilbert modular forms of full level and of weight 2 or greater, the product of two Hecke eigenforms is not a Hecke eigenform except for finitely many real quadratic fields and finitely many weights. We show that for \({\mathbb {Q}}(\sqrt{5})\) there are exactly two such identities.

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Authors and Affiliations

  1. Department of Mathematics, The University of Arizona, Tucson, AZ, 85721-0089, USA

    Kirti Joshi

  2. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Yichao Zhang

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  1. Kirti Joshi
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  2. Yichao Zhang
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Correspondence to Yichao Zhang.

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Y. Zhang: partially supported by HIT Youth Talent Start-Up Grant and Grant of Technology Division of Harbin (RC2016XK001001).

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Joshi, K., Zhang, Y. Eigenform product identities for Hilbert modular forms. Math. Z. 293, 1161–1179 (2019). https://doi.org/10.1007/s00209-018-2214-y

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  • DOI: https://doi.org/10.1007/s00209-018-2214-y

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