Abstract
In this paper, we give an extension of the classical story of the elliptic modular function to the Hilbert modular case for . We construct the period mapping for a family of surfaces with complex parameters and . The inverse correspondence of the period mapping gives a system of generators of Hilbert modular functions for . Moreover, we show an explicit expression of this inverse correspondence by theta constants.
Citation
Atsuhira Nagano. "A theta expression of the Hilbert modular functions for via the periods of surfaces." Kyoto J. Math. 53 (4) 815 - 843, Winter 2013. https://doi.org/10.1215/21562261-2366102
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