Twisted traces of modular functions on hyperbolic 3-space.
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| Title: | Twisted traces of modular functions on hyperbolic 3-space. |
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| Authors: | Herrero, S.1,2 (AUTHOR) sebastian.herrero.m@gmail.com, Imamoḡlu, Ö.2 (AUTHOR) ozlem@math.ethz.ch, von Pippich, A.-M.3 (AUTHOR) anna.pippich@uni-konstanz.de, Schwagenscheidt, M.2 (AUTHOR) mschwagen@ethz.ch |
| Source: | Journal of Number Theory. Feb2026, Vol. 279, p154-169. 16p. |
| Subjects: | Modular functions, Eisenstein series, Harmonic functions, Hyperbolic spaces, Mathematical functions, Fourier analysis, Dirichlet series |
| Abstract: | We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic 3-space and show that they are essentially given by Fourier coefficients of the j -invariant. From this we deduce that the twisted traces of these harmonic modular functions are integers. Additionally, we compute the twisted traces of Eisenstein series on hyperbolic 3-space in terms of Dirichlet L -functions and divisor sums. [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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 187866132 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Twisted traces of modular functions on hyperbolic 3-space. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Herrero%2C+S%2E%22">Herrero, S.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> sebastian.herrero.m@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Imamoḡlu%2C+Ö%2E%22">Imamoḡlu, Ö.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> ozlem@math.ethz.ch</i><br /><searchLink fieldCode="AR" term="%22von+Pippich%2C+A%2E-M%2E%22">von Pippich, A.-M.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> anna.pippich@uni-konstanz.de</i><br /><searchLink fieldCode="AR" term="%22Schwagenscheidt%2C+M%2E%22">Schwagenscheidt, M.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> mschwagen@ethz.ch</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Feb2026, Vol. 279, p154-169. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Modular+functions%22">Modular functions</searchLink><br /><searchLink fieldCode="DE" term="%22Eisenstein+series%22">Eisenstein series</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+functions%22">Harmonic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Hyperbolic+spaces%22">Hyperbolic spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+analysis%22">Fourier analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Dirichlet+series%22">Dirichlet series</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic 3-space and show that they are essentially given by Fourier coefficients of the j -invariant. From this we deduce that the twisted traces of these harmonic modular functions are integers. Additionally, we compute the twisted traces of Eisenstein series on hyperbolic 3-space in terms of Dirichlet L -functions and divisor sums. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jnt.2025.06.010 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 154 Subjects: – SubjectFull: Modular functions Type: general – SubjectFull: Eisenstein series Type: general – SubjectFull: Harmonic functions Type: general – SubjectFull: Hyperbolic spaces Type: general – SubjectFull: Mathematical functions Type: general – SubjectFull: Fourier analysis Type: general – SubjectFull: Dirichlet series Type: general Titles: – TitleFull: Twisted traces of modular functions on hyperbolic 3-space. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Herrero, S. – PersonEntity: Name: NameFull: Imamoḡlu, Ö. – PersonEntity: Name: NameFull: von Pippich, A.-M. – PersonEntity: Name: NameFull: Schwagenscheidt, M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0022314X Numbering: – Type: volume Value: 279 Titles: – TitleFull: Journal of Number Theory Type: main |
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