Bounds for sets with no polynomial progressions

Sarah Peluse

doi:10.1017/fmp.2020.11

Bounds for sets with no polynomial progressions

Sarah Peluse

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Let be polynomials with distinct degrees, each having zero constant term. We show that any subset A of with no nontrivial progressions of the form has size. Along the way, we prove a general result controlling weighted counts of polynomial progressions by Gowers norms.

Original language	English (US)
Article number	e16
Journal	Forum of Mathematics, Pi
DOIs	https://doi.org/10.1017/fmp.2020.11
State	Accepted/In press - 2021

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

11B30
2020 Mathematics Subject Classification

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10.1017/fmp.2020.11

Cite this

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title = "Bounds for sets with no polynomial progressions",

abstract = "Let be polynomials with distinct degrees, each having zero constant term. We show that any subset A of with no nontrivial progressions of the form has size. Along the way, we prove a general result controlling weighted counts of polynomial progressions by Gowers norms.",

keywords = "11B30, 2020 Mathematics Subject Classification",

author = "Sarah Peluse",

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year = "2021",

doi = "10.1017/fmp.2020.11",

language = "English (US)",

journal = "Forum of Mathematics, Pi",

issn = "2050-5086",

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AU - Peluse, Sarah

N1 - Publisher Copyright: © The Author(s), 2020. Published by Cambridge University Press.

PY - 2021

Y1 - 2021

N2 - Let be polynomials with distinct degrees, each having zero constant term. We show that any subset A of with no nontrivial progressions of the form has size. Along the way, we prove a general result controlling weighted counts of polynomial progressions by Gowers norms.

AB - Let be polynomials with distinct degrees, each having zero constant term. We show that any subset A of with no nontrivial progressions of the form has size. Along the way, we prove a general result controlling weighted counts of polynomial progressions by Gowers norms.

KW - 11B30

KW - 2020 Mathematics Subject Classification

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DO - 10.1017/fmp.2020.11

M3 - Article

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SN - 2050-5086

JO - Forum of Mathematics, Pi

JF - Forum of Mathematics, Pi

M1 - e16

ER -

Bounds for sets with no polynomial progressions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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