A bilinear estimate in $\mathbb{F}_p$ Article Swipe
Necef Kavrut
,
Shukun Wu
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.07925
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.07925
We improve an $L^2\times L^2\to L^2$ estimate for a certain bilinear operator in the finite field of size $p$, where $p$ is a prime sufficiently large. Our method carefully picks the variables to apply the Cauchy-Schwarz inequality. As a corollary, we show that there exists a quadratic progression $x,x+y,x+y^2$ for nonzero $y$ inside any subset of $\mathbb{F}_p$ of density $\gtrsim p^{-1/8}$
Related Topics
Concepts
Corollary
Bilinear interpolation
Mathematics
Finite field
Operator (biology)
Prime (order theory)
Quadratic equation
Combinatorics
Field (mathematics)
Bilinear form
Cauchy–Schwarz inequality
Pure mathematics
Inequality
Discrete mathematics
Mathematical analysis
Statistics
Geometry
Gene
Biochemistry
Repressor
Transcription factor
Chemistry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2401.07925
- https://arxiv.org/pdf/2401.07925
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4390962518
All OpenAlex metadata
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https://openalex.org/W4390962518Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2401.07925Digital Object Identifier
- Title
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A bilinear estimate in $\mathbb{F}_p$Work title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
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2024-01-15Full publication date if available
- Authors
-
Necef Kavrut, Shukun WuList of authors in order
- Landing page
-
https://arxiv.org/abs/2401.07925Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2401.07925Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2401.07925Direct OA link when available
- Concepts
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Corollary, Bilinear interpolation, Mathematics, Finite field, Operator (biology), Prime (order theory), Quadratic equation, Combinatorics, Field (mathematics), Bilinear form, Cauchy–Schwarz inequality, Pure mathematics, Inequality, Discrete mathematics, Mathematical analysis, Statistics, Geometry, Gene, Biochemistry, Repressor, Transcription factor, ChemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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