Hybrid subconvex bounds for GL3 × GL1 twisted L-functions and their applications.
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| Title: | Hybrid subconvex bounds for GL3 × GL1 twisted L-functions and their applications. |
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| Authors: | Hou, Fei1 (AUTHOR) fhou@xaut.edu.cn, Lü, GuangShi2 (AUTHOR) gslv@sdu.edu.cn |
| Source: | Journal of Number Theory. Apr2026, Vol. 281, p283-320. 38p. |
| Subjects: | L-functions, Automorphic forms, Mathematical formulas, Analytic number theory, Fourier analysis |
| Abstract: | Let P , M be two primes such that (P , M) = 1. Let f be a Hecke newform of level P , and χ a primitive Dirichlet character modulo M. In this paper, we study the hybrid subconvexity problem for L (s , sym 2 f ⊗ χ) simultaneously in the level and conductor aspects. Among other things, we prove that the hybrid subconvex bound can be achieved, so long as M ε < P < M 3 / 20. One of the key ingredients is that we develop the classical level aspect version of the Voronoĭ formula for the symmetric square lift in an alternative way by tracing back to its geometric nature. As the direct applications, we obtained the subconvex bound for L (s , f ⊗ f ⊗ χ) simultaneously in the level and conductor aspects and the non-obvious bound for the problem of distinguishing modular forms f and f χ based on their first Fourier coefficients. [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: 189762248 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Hybrid subconvex bounds for GL3 × GL1 twisted L-functions and their applications. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hou%2C+Fei%22">Hou, Fei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fhou@xaut.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lü%2C+GuangShi%22">Lü, GuangShi</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> gslv@sdu.edu.cn</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, p283-320. 38p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22L-functions%22">L-functions</searchLink><br /><searchLink fieldCode="DE" term="%22Automorphic+forms%22">Automorphic forms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+formulas%22">Mathematical formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Analytic+number+theory%22">Analytic number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+analysis%22">Fourier analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let P , M be two primes such that (P , M) = 1. Let f be a Hecke newform of level P , and χ a primitive Dirichlet character modulo M. In this paper, we study the hybrid subconvexity problem for L (s , sym 2 f ⊗ χ) simultaneously in the level and conductor aspects. Among other things, we prove that the hybrid subconvex bound can be achieved, so long as M ε < P < M 3 / 20. One of the key ingredients is that we develop the classical level aspect version of the Voronoĭ formula for the symmetric square lift in an alternative way by tracing back to its geometric nature. As the direct applications, we obtained the subconvex bound for L (s , f ⊗ f ⊗ χ) simultaneously in the level and conductor aspects and the non-obvious bound for the problem of distinguishing modular forms f and f χ based on their first Fourier coefficients. [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.2025.09.014 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 38 StartPage: 283 Subjects: – SubjectFull: L-functions Type: general – SubjectFull: Automorphic forms Type: general – SubjectFull: Mathematical formulas Type: general – SubjectFull: Analytic number theory Type: general – SubjectFull: Fourier analysis Type: general Titles: – TitleFull: Hybrid subconvex bounds for GL3 × GL1 twisted L-functions and their applications. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hou, Fei – PersonEntity: Name: NameFull: Lü, GuangShi 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 |
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