A theta expression of the Hilbert modular functions for √ 5 via the periods of K3 surfaces

Atsuhira Nagano

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    In this paper, we give an extension of the classical story of the elliptic modular function to the Hilbertmodular case forQ( √ 5).We construct the period mapping for a family F = {S(X,Y )} ofK3 surfaces with 2 complex parametersX and Y . The inverse correspondence of the period mapping gives a system of generators of Hilbert modular functions forQ( √ 5). Moreover, we show an explicit expression of this inverse correspondence by theta constants.

    Original languageEnglish
    Pages (from-to)815-843
    Number of pages29
    JournalKyoto Journal of Mathematics
    Issue number4
    Publication statusPublished - 2013 Dec


    ASJC Scopus subject areas

    • Mathematics(all)

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