The Furstenberg-Sárközy theorem for intersective polynomials in function fields

DOI10.1016/J.FFA.2019.03.002zbMATH Open1503.11132OpenAlexW2923648553MaRDI QIDQ2422185

Guoquan Li

Publication date: 18 June 2019

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2019.03.002

zbMATH Keywords

function fieldexponential sumHardy-Littlewood circle methodFurstenberg-Sárközy theoremdensity incrementintersective polynomial

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Arithmetic theory of polynomial rings over finite fields (11T55)

Cites Work

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• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Van der Corput's difference theorem
• Difference sets without \(\kappa\)-th powers
• Diophantine approximation of polynomials over \(\mathbb{F}_q[t]\) satisfying a divisibility condition
• On sets of polynomials whose difference set contains no squares
• Sárközy's Theorem in Function Fields
• Waring's problem in function fields
• Intersective sets given by a polynomial
• On Sets of Natural Numbers Whose Difference Set Contains No Squares
• On difference sets of sequences of integers. I
• A maximal extension of the best-known bounds for the Furstenberg–Sárközy theorem
• Problems and Results on Intersective Sets

Related Items (8)

[[Publication:3308092|Title not available (Why is that?)]] ⋮ The Pintz–Steiger–Szemerédi estimate for intersective quadratic polynomials in function fields ⋮ An improvement to Chevalley's theorem with restricted variables ⋮ Interspersion in Suffridge's polynomial theory ⋮ A polynomial Sárközy-Furstenberg theorem with upper bounds ⋮ On recurrence in positive characteristic ⋮ Intersective polynomials along the irreducibles in function fields ⋮ A partial improvement of the Ax-Katz theorem

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