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On algebraicity of special values of symmetric 4-th and 6-th power L-functions for \(\mathrm {GL}(2)\)

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Abstract

We prove an algebraicity of special values of symmetric 4-th and 6-th power L-functions of Hilbert cusp forms using its symmetric power lifting and several algebraicity results on special values of automorphic L-functions.

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Acknowledgements

This paper was partly written while the author stayed at National University of Singapore. The author would like to thank the people in NUS for their warm hospitality. He also would like to thank to Masaaki Furusawa, Atsushi Ichino and Abhishek Saha for helpful comments. The author would like to express his deep gratitude to Shih–Yu Chen for explaining to the author the argument in Remark 14 and pointing out a lot of inaccuracies. Finally, the author is grateful to the anonymous referee for pointing out inaccuracies and for a lot of helpful comments.

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  1. Department of Mathematics, Kobe University, 1-1, Rokkodai-cho, Naka-ku, Kobe, 657-8501, Japan

    Kazuki Morimoto

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  1. Kazuki Morimoto
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Correspondence to Kazuki Morimoto.

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The research of the author was supported in part by Grant-in-Aid for Young Scientists (B) 17K14166 and Kobe University Long Term Overseas Visiting Program for Young Researchers Fund.

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Morimoto, K. On algebraicity of special values of symmetric 4-th and 6-th power L-functions for \(\mathrm {GL}(2)\). Math. Z. 299, 1331–1350 (2021). https://doi.org/10.1007/s00209-021-02727-5

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