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Congruences of Siegel Eisenstein series of degree two

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Abstract

In this paper we study congruences between Siegel Eisenstein series and Siegel cusp forms for \(\mathrm{Sp}_4(\mathbb {Z})\).

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Acknowledgements

The author would like to thank Florian Herzig, Hidenori Katsurada, Can-Ho Kim, Iwao Kimura, Ariel Weiss for helpful comments and many valuable discussions. In particular, Herzig and Weiss kindly informed the author an error of [4] for the irreducibility of mod p Galois representations attached to RAESDC automorphic representations. This work started when the author visited Pavel Guerzhoy at University of Hawaii. The author would also like to thank him for valuable discussions and the university for the incredible hospitality. Finally, the author would like to the referee for reading the article carefully to correct and improve greatly.

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  1. Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba-Ku, Sendai, 980-8578, Japan

    Takuya Yamauchi

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Correspondence to Takuya Yamauchi.

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The author is partially supported by JSPS KAKENHI Grant Number (B) No. 19H01778.

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Yamauchi, T. Congruences of Siegel Eisenstein series of degree two. manuscripta math. 166, 589–603 (2021). https://doi.org/10.1007/s00229-020-01256-5

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