Revista Matemática Iberoamericana


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Volume 22, Issue 1, 2006, pp. 357–368
DOI: 10.4171/RMI/460

Published online: 2006-04-30

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

Shoyu Nagaoka[1]

(1) Kinki University, Osaka, Japan

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.

Keywords: Hilbert modular forms, modular forms mod $p$

Nagaoka Shoyu: On Hilbert modular forms modulo $p$: explicit ring structure. Rev. Mat. Iberoam. 22 (2006), 357-368. doi: 10.4171/RMI/460