Non-Linear Additive Twists of $\mathrm{GL}_{3}$ Hecke Eigenvalues
| Title: | Non-Linear Additive Twists of $\mathrm{GL}_{3}$ Hecke Eigenvalues |
|---|---|
| Authors: | Kaneko, Ikuya, Leung, Wing Hong |
| Publication Year: | 2023 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Number Theory, 11F66, 11M41 (primary), 11F55 (secondary) |
| More Details: | We bound non-linear additive twists of $\mathrm{GL}_{3}$ Hecke eigenvalues, improving upon the work of Kumar-Mallesham-Singh (2022). The proof employs the DFI circle method with standard manipulations (Voronoi, Cauchy-Schwarz, lengthening, and additive reciprocity). The main novelty includes the conductor lowering mechanism, albeit sacrificing some savings to remove an analytic oscillation, followed by the iteration ad infinitum of Cauchy-Schwarz and Poisson. The resulting character sums are estimated via the work of Adolphson-Sperber (1993). As an application, we prove nontrivial bounds for the first moment of $\mathrm{GL}_{3}$ Hardy's function, which corresponds to the cubic moment of Hardy's function studied by Ivi\'{c} (2012). Comment: 26 pages. LaTeX2e |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2311.13788 |
| Accession Number: | edsarx.2311.13788 |
| Database: | arXiv |
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| Items | – Name: Title Label: Title Group: Ti Data: Non-Linear Additive Twists of $\mathrm{GL}_{3}$ Hecke Eigenvalues – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kaneko%2C+Ikuya%22">Kaneko, Ikuya</searchLink><br /><searchLink fieldCode="AR" term="%22Leung%2C+Wing+Hong%22">Leung, Wing Hong</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2023 – Name: Subset Label: Collection Group: HoldingsInfo Data: Mathematics – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Mathematics+-+Number+Theory%22">Mathematics - Number Theory</searchLink><br /><searchLink fieldCode="DE" term="%2211F66%2C+11M41+%28primary%29%2C+11F55+%28secondary%29%22">11F66, 11M41 (primary), 11F55 (secondary)</searchLink> – Name: Abstract Label: Description Group: Ab Data: We bound non-linear additive twists of $\mathrm{GL}_{3}$ Hecke eigenvalues, improving upon the work of Kumar-Mallesham-Singh (2022). The proof employs the DFI circle method with standard manipulations (Voronoi, Cauchy-Schwarz, lengthening, and additive reciprocity). The main novelty includes the conductor lowering mechanism, albeit sacrificing some savings to remove an analytic oscillation, followed by the iteration ad infinitum of Cauchy-Schwarz and Poisson. The resulting character sums are estimated via the work of Adolphson-Sperber (1993). As an application, we prove nontrivial bounds for the first moment of $\mathrm{GL}_{3}$ Hardy's function, which corresponds to the cubic moment of Hardy's function studied by Ivi\'{c} (2012).<br />Comment: 26 pages. LaTeX2e – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2311.13788" linkWindow="_blank">http://arxiv.org/abs/2311.13788</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.2311.13788 |
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| RecordInfo | BibRecord: BibEntity: Subjects: – SubjectFull: Mathematics - Number Theory Type: general – SubjectFull: 11F66, 11M41 (primary), 11F55 (secondary) Type: general Titles: – TitleFull: Non-Linear Additive Twists of $\mathrm{GL}_{3}$ Hecke Eigenvalues Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kaneko, Ikuya – PersonEntity: Name: NameFull: Leung, Wing Hong IsPartOfRelationships: – BibEntity: Dates: – D: 22 M: 11 Type: published Y: 2023 |
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