Geodesic
Double integrals on a weighted projective plane and Hilbert modular functions for $\mathbb {Q}(\sqrt {5})$
Atsuhira Nagano1
1 Department of Mathematics Waseda University Okubo 3-4-1, Shinjuku-ku Tokyo 169-8555, Japan
Acta Arithmetica, Tome 167 (2015) no. 4, pp. 327-345.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The aim of this paper is to give an explicit extension of classical elliptic integrals to the Hilbert modular case for $\mathbb {Q}(\sqrt {5})$. 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 $\mathbb {P}(1:1:2)$ 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 $\mathbb {C}^2$.
DOI : 10.4064/aa167-4-2
Keywords: paper explicit extension classical elliptic integrals hilbert modular mathbb sqrt study family kummer surfaces corresponding humbert surface invariant complex parameters kummer surface given double covering weighted projective space mathbb branched along parabola quintic curve period mapping family given double integrals algebraic function chambers coming arrangement parabola quintic curve nbsp mathbb

Atsuhira Nagano 1

1 Department of Mathematics Waseda University Okubo 3-4-1, Shinjuku-ku Tokyo 169-8555, Japan 
@article{10_4064_aa167_4_2,
     author = {Atsuhira Nagano},
     title = {Double integrals on a weighted projective plane
 and {Hilbert} modular functions for $\mathbb {Q}(\sqrt {5})$},
     journal = {Acta Arithmetica},
     pages = {327--345},
     publisher = {mathdoc},
     volume = {167},
     number = {4},
     year = {2015},
     doi = {10.4064/aa167-4-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa167-4-2/}
}
TY  - JOUR
AU  - Atsuhira Nagano
TI  - Double integrals on a weighted projective plane
 and Hilbert modular functions for $\mathbb {Q}(\sqrt {5})$
JO  - Acta Arithmetica
PY  - 2015
SP  - 327
EP  - 345
VL  - 167
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa167-4-2/
DO  - 10.4064/aa167-4-2
LA  - en
ID  - 10_4064_aa167_4_2
ER  - 
%0 Journal Article
%A Atsuhira Nagano
%T Double integrals on a weighted projective plane
 and Hilbert modular functions for $\mathbb {Q}(\sqrt {5})$
%J Acta Arithmetica
%D 2015
%P 327-345
%V 167
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa167-4-2/
%R 10.4064/aa167-4-2
%G en
%F 10_4064_aa167_4_2
Atsuhira Nagano. Double integrals on a weighted projective plane
 and Hilbert modular functions for $\mathbb {Q}(\sqrt {5})$. Acta Arithmetica, Tome 167 (2015) no. 4, pp. 327-345. doi : 10.4064/aa167-4-2. http://geodesic.mathdoc.fr/articles/10.4064/aa167-4-2/

Cité par Sources :