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Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms

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Abstract

In this article, we study simultaneous sign changes of the Fourier coefficients of two Hilbert cusp forms of different non-parallel weights. We also study simultaneous non-vanishing of Fourier coefficients of two distinct non-zero primitive Hilbert cuspidal non-CM eigenforms of integral weights at powers of prime ideals.

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Acknowledgements

The authors would like to express their gratitude to an anonymous referee for his/her careful reading of our manuscript and for their suggestions which improved the presentation of the article. The research of the second author was supported partly by the start up research grant of IIT Hyderabad.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, 502285, India

    Surjeet Kaushik & Narasimha Kumar

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  1. Surjeet Kaushik
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  2. Narasimha Kumar
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Correspondence to Narasimha Kumar.

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Kaushik, S., Kumar, N. Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms. Arch. Math. 112, 241–248 (2019). https://doi.org/10.1007/s00013-018-1275-9

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  • DOI: https://doi.org/10.1007/s00013-018-1275-9

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