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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-4-2,
author = {Atsuhira Nagano},
title = {Double integrals on a weighted projective plane and Hilbert modular functions for $\mathbb{Q}$ ($\surd$5)},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {327-345},
zbl = {06414116},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-4-2}
}
Atsuhira Nagano. Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5). Acta Arithmetica, Tome 168 (2015) pp. 327-345. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-4-2/