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Implementations of forgetful maps on modular curves.

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Title: Implementations of forgetful maps on modular curves.
Authors: JEON, Daeyeol1
Source: Proceedings of the Japan Academy, Series A: Mathematical Sciences. Dec2025, Vol. 101 Issue 10, p51-56. 6p.
Subjects: Modular forms, Mathematical mappings, Automorphic forms, Mathematics, Mathematicians
Abstract: In this paper, we aim to implement the forgetful maps from X1(N) to X0(N) and from to Xð1Þ using the Hauptmoduls of X1ðNÞ, X0ðNÞ, and Xð1Þ. This approach is similar to the work of Kim and Koo [KK4], who constructed the Hauptmoduls for X1ðNÞ through various methods and utilized the known eta quotients as the Hauptmoduls for X0ðNÞ. However we use other Hauptmoduls for X1ðNÞ and X0ðNÞ which can be constructed by using the generators of the function field of X1ðNÞ introduced by Baaziz [B]. [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy 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: Implementations of forgetful maps on modular curves.
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  Data: <searchLink fieldCode="DE" term="%22Modular+forms%22">Modular forms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+mappings%22">Mathematical mappings</searchLink><br /><searchLink fieldCode="DE" term="%22Automorphic+forms%22">Automorphic forms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematicians%22">Mathematicians</searchLink>
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  Data: In this paper, we aim to implement the forgetful maps from X1(N) to X0(N) and from to Xð1Þ using the Hauptmoduls of X1ðNÞ, X0ðNÞ, and Xð1Þ. This approach is similar to the work of Kim and Koo [KK4], who constructed the Hauptmoduls for X1ðNÞ through various methods and utilized the known eta quotients as the Hauptmoduls for X0ðNÞ. However we use other Hauptmoduls for X1ðNÞ and X0ðNÞ which can be constructed by using the generators of the function field of X1ðNÞ introduced by Baaziz [B]. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy 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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        Value: 10.3792/pjaa.101.010
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      – Code: eng
        Text: English
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    Subjects:
      – SubjectFull: Modular forms
        Type: general
      – SubjectFull: Mathematical mappings
        Type: general
      – SubjectFull: Automorphic forms
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      – SubjectFull: Mathematics
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      – TitleFull: Implementations of forgetful maps on modular curves.
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              M: 12
              Text: Dec2025
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              Y: 2025
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