On monochromatic solutions of some nonlinear equations in \(\mathbb Z/p\mathbb Z\)

DOI10.1134/S0001434610090336zbMath1232.05225arXiv0909.3269MaRDI QIDQ650322

Ilya D. Shkredov

Publication date: 25 November 2011

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3269

zbMATH Keywords

Fourier transformRamsey theorycoloringtrigonometric sumDirichlet characterCauchy-Bunyakovskii inequalitymonochromatic solution

Mathematics Subject Classification ID

Extremal set theory (05D05) Other combinatorial number theory (11B75) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Ramsey theory (05D10) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (9)

Three-term polynomial progressions in subsets of finite fields ⋮ Combinatorial Nullstellensatz approach to polynomial expansion ⋮ Some combinatorial number theory problems over finite valuation rings ⋮ Improved estimates for polynomial Roth type theorems in finite fields ⋮ Combinatorial problems in finite fields and Sidon sets ⋮ A note on the size of the set \(A^2+A\) ⋮ Monochromatic sum and product in \(\mathbb{Z} / m \mathbb{Z}\) ⋮ A Hörmander type theorem in finite fields ⋮ Products of Differences over Arbitrary Finite Fields

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