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Algebraicity of critical values of adjoint L-functions for \(\mathrm{GSp}_4\)

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Abstract

We prove an algebraicity result for certain critical value of adjoint L-functions for \(\mathrm{GSp}_4\) over a totally real number field in terms of the Petersson norm of normalized generic cuspidal newforms on \(\mathrm{GSp}_4\). As an application, we establish an algebraic version of the Lapid–Mao conjecture for Whittaker–Fourier coefficients of cusp forms on \(\mathrm{GSp}_4\).

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Acknowledgements

The author would like to thank Yao Cheng and Atsushi Ichino for suggestions and helpful conversations. Thanks are also due to the referee for the helpful comments.

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  1. Institute of Mathematics Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan, ROC

    Shih-Yu Chen

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Chen, SY. Algebraicity of critical values of adjoint L-functions for \(\mathrm{GSp}_4\). Ramanujan J 59, 883–931 (2022). https://doi.org/10.1007/s11139-022-00582-4

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