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A Kronecker congruence relation for modular functions of higher level and genus.

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Title: A Kronecker congruence relation for modular functions of higher level and genus.
Authors: Jung, Ho Yun1 (AUTHOR) hoyunjung@dankook.ac.kr, Koo, Ja Kyung2 (AUTHOR) jkgoo@kaist.ac.kr, Shin, Dong Hwa1,3 (AUTHOR) dhshin@hufs.ac.kr
Source: Journal of Number Theory. Jan2026, Vol. 278, p875-892. 18p.
Subjects: Modular functions, Congruence lattices, Holomorphic functions, Elliptic functions, Polynomials
Abstract: Let j be the elliptic modular function, a weakly holomorphic modular function for SL 2 (Z). Weber showed that for each prime p the modular polynomial Φ p (x , y) of j satisfies what is known as the Kronecker congruence relation Φ p (x , y) ≡ (x p − y) (x − y p) (mod p Z [ x , y ]). We give a generalization of this congruence applicable to certain weakly holomorphic modular functions of higher level in terms of integrality over Z [ j ]. [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: A Kronecker congruence relation for modular functions of higher level and genus.
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  Data: <searchLink fieldCode="AR" term="%22Jung%2C+Ho+Yun%22">Jung, Ho Yun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hoyunjung@dankook.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Koo%2C+Ja+Kyung%22">Koo, Ja Kyung</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> jkgoo@kaist.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Shin%2C+Dong+Hwa%22">Shin, Dong Hwa</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> dhshin@hufs.ac.kr</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Jan2026, Vol. 278, p875-892. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Modular+functions%22">Modular functions</searchLink><br /><searchLink fieldCode="DE" term="%22Congruence+lattices%22">Congruence lattices</searchLink><br /><searchLink fieldCode="DE" term="%22Holomorphic+functions%22">Holomorphic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+functions%22">Elliptic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink>
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  Data: Let j be the elliptic modular function, a weakly holomorphic modular function for SL 2 (Z). Weber showed that for each prime p the modular polynomial Φ p (x , y) of j satisfies what is known as the Kronecker congruence relation Φ p (x , y) ≡ (x p − y) (x − y p) (mod p Z [ x , y ]). We give a generalization of this congruence applicable to certain weakly holomorphic modular functions of higher level in terms of integrality over Z [ j ]. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  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.2025.05.011
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 18
        StartPage: 875
    Subjects:
      – SubjectFull: Modular functions
        Type: general
      – SubjectFull: Congruence lattices
        Type: general
      – SubjectFull: Holomorphic functions
        Type: general
      – SubjectFull: Elliptic functions
        Type: general
      – SubjectFull: Polynomials
        Type: general
    Titles:
      – TitleFull: A Kronecker congruence relation for modular functions of higher level and genus.
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            NameFull: Jung, Ho Yun
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            NameFull: Koo, Ja Kyung
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            NameFull: Shin, Dong Hwa
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            – D: 01
              M: 01
              Text: Jan2026
              Type: published
              Y: 2026
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              Value: 278
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            – TitleFull: Journal of Number Theory
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