General form of Humbert's modular equation for curves with real multiplication of Δ = 5

Kiichiro Hashimoto*, Yukiko Sakai

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

We study Humbert's modular equation which characterizes curves of genus two having real multiplication by the quadratic order of discriminant 5. We give it a simple, but general expression as a polynomial in x1;.. .; x6 the coordinate of the Weierstrass points, and show that it is invariant under a transitive permutation group of degree 6 isomorphic to S{fraktur}5. We also prove the rationality of the hypersurface in P5 defined by the generalized modular equation.

本文言語English
ページ(範囲)171-176
ページ数6
ジャーナルProceedings of the Japan Academy Series A: Mathematical Sciences
85
10
DOI
出版ステータスPublished - 2009 12
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「General form of Humbert's modular equation for curves with real multiplication of Δ = 5」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル