Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms
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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.
KeywordsHilbert modular forms Fourier coefficients Sign changes Non-vanishing
Mathematics Subject ClassificationPrimary 11F03 11F30 Secondary 11F41
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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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