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

Atsuhira Nagano

Acta Arithmetica (2015)

  • Volume: 167, Issue: 4, page 327-345
  • ISSN: 0065-1036

Abstract

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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.

How to cite

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Atsuhira Nagano. "Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)." Acta Arithmetica 167.4 (2015): 327-345. <http://eudml.org/doc/286412>.

@article{AtsuhiraNagano2015,
abstract = {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.},
author = {Atsuhira Nagano},
journal = {Acta Arithmetica},
keywords = {Hilbert modular functions; Kummer surfaces; elliptic integrals},
language = {eng},
number = {4},
pages = {327-345},
title = {Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)},
url = {http://eudml.org/doc/286412},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Atsuhira Nagano
TI - Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 4
SP - 327
EP - 345
AB - 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.
LA - eng
KW - Hilbert modular functions; Kummer surfaces; elliptic integrals
UR - http://eudml.org/doc/286412
ER -

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