Parameters of solvable automorphic forms.
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| Title: | Parameters of solvable automorphic forms. |
|---|---|
| Authors: | Uttenthal, Peter Vang1 (AUTHOR) petervang@math.au.dk |
| Source: | Journal of Number Theory. Apr2026, Vol. 281, p771-794. 24p. |
| Subjects: | Automorphic forms, Modular forms |
| Abstract: | In a letter from Tate to Serre dated March 26, 1974, Tate suggested a classification of weight one modular forms of prime level in terms of their associated odd Artin representations. This paper carries out an analogous classification of Maass wave forms of prime power level in terms of complex even representations. The parameters are identified with techniques from class field theory and Galois representations. The classification reveals that there exist distinct Maass cusp forms of tetrahedral type on Γ 1 (ℓ) that remain inequivalent modulo 3 for ℓ = 7687 , 16363 and 20887, and that these ℓ are the three smallest such primes. [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: 189762275 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Parameters of solvable automorphic forms. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Uttenthal%2C+Peter+Vang%22">Uttenthal, Peter Vang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> petervang@math.au.dk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Apr2026, Vol. 281, p771-794. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Automorphic+forms%22">Automorphic forms</searchLink><br /><searchLink fieldCode="DE" term="%22Modular+forms%22">Modular forms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In a letter from Tate to Serre dated March 26, 1974, Tate suggested a classification of weight one modular forms of prime level in terms of their associated odd Artin representations. This paper carries out an analogous classification of Maass wave forms of prime power level in terms of complex even representations. The parameters are identified with techniques from class field theory and Galois representations. The classification reveals that there exist distinct Maass cusp forms of tetrahedral type on Γ 1 (ℓ) that remain inequivalent modulo 3 for ℓ = 7687 , 16363 and 20887, and that these ℓ are the three smallest such primes. [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.2025.10.016 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 771 Subjects: – SubjectFull: Automorphic forms Type: general – SubjectFull: Modular forms Type: general Titles: – TitleFull: Parameters of solvable automorphic forms. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Uttenthal, Peter Vang IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0022314X Numbering: – Type: volume Value: 281 Titles: – TitleFull: Journal of Number Theory Type: main |
| ResultId | 1 |
