On Hilbert modular forms modulo $p$: explicit ring structure

Shoyu Nagaoka

doi:10.4171/rmi/460

JournalsrmiVol. 22, No. 1pp. 357–368

On Hilbert modular forms modulo $p$ : explicit ring structure

Shoyu Nagaoka
Kinki University, Osaka, Japan

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Abstract

H.P.F. Swinnerton-Dyer determined the structure of the ring of modular forms modulo $p$ in the elliptic modular case. In this paper, the structure of the ring of Hilbert modular forms modulo $p$ is studied. In the case where the discriminant of corresponding quadratic field is 8 (or 5), the explicit structure is determined.

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Shoyu Nagaoka, On Hilbert modular forms modulo $p$ : explicit ring structure. Rev. Mat. Iberoam. 22 (2006), no. 1, pp. 357–368

DOI 10.4171/RMI/460