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

Atsuhira Nagano

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    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
    Volume53
    Issue number4
    DOIs
    Publication statusPublished - 2013 Dec

    Fingerprint

    Modular Functions
    Hilbert Function
    K3 Surfaces
    Correspondence
    Elliptic function
    Generator
    Narrative
    Family

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    A theta expression of the Hilbert modular functions for √ 5 via the periods of K3 surfaces. / Nagano, Atsuhira.

    In: Kyoto Journal of Mathematics, Vol. 53, No. 4, 12.2013, p. 815-843.

    Research output: Contribution to journalArticle

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