### Abstract

We count the number of holomorphic orbi-spheres in the ℤ_{2}-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.

Original language | English |
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Pages (from-to) | 603-629 |

Number of pages | 27 |

Journal | New York Journal of Mathematics |

Volume | 23 |

Publication status | Published - 2017 May 31 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*New York Journal of Mathematics*,

*23*, 603-629.

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*New York Journal of Mathematics*, vol. 23, pp. 603-629.

**Counting of holomorphic orbi-spheres in (Formula presented) and determinant equations.** / Hong, Hansol; Shin, Hyung Seok.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Counting of holomorphic orbi-spheres in (Formula presented) and determinant equations

AU - Hong, Hansol

AU - Shin, Hyung Seok

PY - 2017/5/31

Y1 - 2017/5/31

N2 - We count the number of holomorphic orbi-spheres in the ℤ2-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.

AB - We count the number of holomorphic orbi-spheres in the ℤ2-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.

UR - http://www.scopus.com/inward/record.url?scp=85020819962&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020819962&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85020819962

VL - 23

SP - 603

EP - 629

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -