On a unit group generated by special values of Siegel modular functions

T. Fukuda, Keiichi Komatsu

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    There has been important progress in constructing units and S-units associated to curves of genus 2 or 3. These approaches are based mainly on the consideration of properties of Jacobian varieties associated to hyperelliptic curves of genus 2 or 3. In this paper, we construct a unit group of the ray class field k6 of ℚ(exp(2πi/5)) modulo 6 with full rank by special values of Siegel modular functions and circular units. We note that k6 = ℚ(exp(2πi/15), 5√-24). Our construction of units is number theoretic, and closely based on Shimura's work describing explicitly the Galois actions on the special values of theta functions.

    Original languageEnglish
    Pages (from-to)1207-1212
    Number of pages6
    JournalMathematics of Computation
    Volume69
    Issue number231
    Publication statusPublished - 2000 Jul

    Fingerprint

    Unit Group
    Modular Functions
    Unit
    Genus
    Jacobian Varieties
    Group of Units
    Hyperelliptic Curves
    Theta Functions
    Galois
    Half line
    Modulo
    Curve

    Keywords

    • Computation
    • Siegel modular functions
    • Unit groups

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Applied Mathematics
    • Computational Mathematics

    Cite this

    On a unit group generated by special values of Siegel modular functions. / Fukuda, T.; Komatsu, Keiichi.

    In: Mathematics of Computation, Vol. 69, No. 231, 07.2000, p. 1207-1212.

    Research output: Contribution to journalArticle

    Fukuda, T & Komatsu, K 2000, 'On a unit group generated by special values of Siegel modular functions', Mathematics of Computation, vol. 69, no. 231, pp. 1207-1212.
    Fukuda, T. ; Komatsu, Keiichi. / On a unit group generated by special values of Siegel modular functions. In: Mathematics of Computation. 2000 ; Vol. 69, No. 231. pp. 1207-1212.
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