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- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
- ISSN
- 0025-5858
- eISSN
- 1865-8784
- DOI
- 10.1007/BF02941514
- Publisher site
- See Article on Publisher Site
Abstract
Abh. Math. Sere. Univ. Hamburg 56, 157--168 (1986) By S. NAGAOK~. Introduction This paper is a continuation of [13] in which we studied on the structure of the ring of Hilbert modular forms with integral Fourier coefficients. For a real quadratic field K, we denote by A2~(FK)k the Z-module of symmetric Hilbert modular forms of weight k for ~1[ with rational integral Fourier coefficients. We put A~7(/'K) = 9 AZ(T'K)k, A~:'(T'K) = 9 A~(FKhk. k:>0 k_~0 In [13], the author showed that the ring A~(FQ(~)) is generated by three (e) r elements H2, Ha and//6 over 7Z. and A (FQ(1/D) is gene ated by four elements J2, Je, J10 and J12, where the subscript denotes the weight, and these modular forms are explicitly expressed as polynomials in Eisenstein series. The main purpose of this paper is to determine the structure of the full ring AZ(FK) for two cases K : Our main theorem in the case ~ (~/2) can be stated as follows: Theorem. (1) There existsamodular /orm H 9 el weight 9 low Q (~2) such that the square ~ can be expressed as a polynomial in 1t2, H4, He with integral co- e//icients. The explicit ]orm will
Journal
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Aug 28, 2008