Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)

• Autorzy: Atsuhira Nagano
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to give an explicit extension of classical elliptic integrals to the Hilbert modular case for ℚ (√5). We study a family of Kummer surfaces corresponding to the Humbert surface of invariant 5 with two complex parameters. Our Kummer surface is given by a double covering of the weighted projective space ℙ(1:1:2) branched along a parabola and a quintic curve. The period mapping for our family is given by double integrals of an algebraic function on chambers coming from an arrangement of a parabola and a quintic curve in ℂ².

Kategorie tematyczne

• 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
• 14J28: K 3 surfaces and Enriques surfaces
• 33E05: Elliptic functions and integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 4
• Strony: 327-345

Daty

wydano

2015

Twórcy

autor

Atsuhira Nagano

• Department of Mathematics, Waseda University, Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan

Identyfikatory

DOI

10.4064/aa167-4-2