On Hilbert modular forms with integral Fourier coefficients. (English) Zbl 0623.10018
The author gives explicit generators for the ring of Hilbert modular forms with integral Fourier coefficients for the two real quadratic fields \(\mathbb Q(\sqrt{2})\) and \(\mathbb Q(\sqrt{5})\). This involves explicit computations using elliptic modular forms and Siegel modular forms of genus two.
Reviewer: Rainer Weissauer (Mannheim)
MSC:
| 11F41 | Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces |
| 11F30 | Fourier coefficients of automorphic forms |
Keywords:
generators; ring of Hilbert modular forms; integral Fourier coefficients; real quadratic fieldsReferences:
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