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Extended modular functions and definite form class groups.

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Title: Extended modular functions and definite form class groups.
Authors: Jung, Ho Yun1 (AUTHOR) hoyunjung@dankook.ac.kr, Koo, Ja Kyung2 (AUTHOR) jkgoo@kaist.ac.kr, Shin, Dong Hwa3 (AUTHOR) dhshin@hufs.ac.kr, Shin, Gyucheol4 (AUTHOR) sgc7982@gmail.com
Source: Journal of Number Theory. Mar2026, Vol. 280, p808-824. 17p.
Subjects: Modular functions, Galois theory, Parameterization, Quadratic fields
Abstract: For a positive integer N , we define an extended modular function of level N motivated by physics and investigate its fundamental properties. Let K be an imaginary quadratic field, and let O be an order in K of discriminant D. Let K O , N denote the ray class field of O modulo N O. For N ≥ 3 , we provide an explicit description of the Galois group Gal (K O , N / Q) using special values of extended modular functions of level N and the definite form class group of discriminant D and level N. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: For a positive integer N , we define an extended modular function of level N motivated by physics and investigate its fundamental properties. Let K be an imaginary quadratic field, and let O be an order in K of discriminant D. Let K O , N denote the ray class field of O modulo N O. For N ≥ 3 , we provide an explicit description of the Galois group Gal (K O , N / Q) using special values of extended modular functions of level N and the definite form class group of discriminant D and level N. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jnt.2025.09.002
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 17
        StartPage: 808
    Subjects:
      – SubjectFull: Modular functions
        Type: general
      – SubjectFull: Galois theory
        Type: general
      – SubjectFull: Parameterization
        Type: general
      – SubjectFull: Quadratic fields
        Type: general
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      – TitleFull: Extended modular functions and definite form class groups.
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            NameFull: Koo, Ja Kyung
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            NameFull: Shin, Dong Hwa
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            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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              Value: 280
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            – TitleFull: Journal of Number Theory
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