Finite field models in arithmetic combinatorics -- ten years on
From MaRDI portal
Publication:2512891
DOI10.1016/j.ffa.2014.11.003zbMath1378.11021OpenAlexW2017689808WikidataQ56341572 ScholiaQ56341572MaRDI QIDQ2512891
Publication date: 30 January 2015
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.ffa.2014.11.003
Research exposition (monographs, survey articles) pertaining to number theory (11-02) Additive bases, including sumsets (11B13) Arithmetic progressions (11B25) Arithmetic combinatorics; higher degree uniformity (11B30)
Related Items (14)
Generalizations of Fourier analysis, and how to apply them ⋮ Finding Patterns Avoiding Many Monochromatic Constellations ⋮ New applications of the polynomial method: The cap set conjecture and beyond ⋮ Approximate cohomology ⋮ A refinement of Cauchy-Schwarz complexity ⋮ On higher-order Fourier analysis in characteristic p ⋮ Partition and analytic rank are equivalent over large fields ⋮ A bilinear Bogolyubov theorem ⋮ The Erdős–Moser Sum-free Set Problem ⋮ Unnamed Item ⋮ Caps and progression-free sets in \(\mathbb{Z}_m^n\) ⋮ Essential components in vector spaces over finite fields ⋮ Bootstrapping partition regularity of linear systems ⋮ Bounds in Cohen's idempotent theorem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Equivalence of polynomial conjectures in additive combinatorics
- The inverse conjecture for the Gowers norm over finite fields in low characteristic
- A probabilistic technique for finding almost-periods of convolutions
- Linear forms and higher-degree uniformity for functions on \(\mathbb F^n_p\)
- The inverse conjecture for the Gowers norm over finite fields via the correspondence principle
- On Roth's theorem on progressions
- A new proof of Szemerédi's theorem for arithmetic progressions of length four
- Extensions of generalized product caps
- An improved construction of progression-free sets
- A polynomial bound in Freiman's theorem.
- On subsets of finite Abelian groups with no 3-term arithmetic progressions
- The structure of approximate groups.
- On the Bogolyubov-Ruzsa lemma
- On triples in arithmetic progression
- Roth's theorem in many variables
- New proofs of Plünnecke-type estimates for product sets in groups
- An inverse theorem for the uniformity seminorms associated with the action of \(\mathbb F_p^\infty\)
- Nonconventional ergodic averages and nilmanifolds
- The primes contain arbitrarily long arithmetic progressions
- The Freiman-Ruzsa theorem over finite fields
- New bounds on cap sets
- Approximate groups and doubling metrics
- Inverse Conjecture for the Gowers norm is false
- Translation invariant equations and the method of Sanders
- A Sum–Product Theorem in Function Fields
- A Note on Elkin’s Improvement of Behrend’s Construction
- Green's sumset problem at density one half
- AN INVERSE THEOREM FOR THE GOWERSU4-NORM
- Green–Tao theorem in function fields
- LINEAR FORMS AND QUADRATIC UNIFORMITY FOR FUNCTIONS ON
- On Sums of Generating Sets in ℤ2n
- A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1.
- Waring's problem in function fields
- Universal characteristic factors and Furstenberg averages
- Freiman's Theorem in Finite Fields via Extremal Set Theory
- The distribution of polynomials over finite fields, with applications to the Gowers norms
- An equivalence between inverse sumset theorems and inverse conjectures for theU3norm
- New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries
- On sets of integers containing k elements in arithmetic progression
- On difference sets of sequences of integers. I
- Limits of functions on groups
- Testing subgraphs in large graphs
- The structure theory of set addition revisited
- An Entropic Proof of Chang's Inequality
- Sampling-Based Proofs of Almost-Periodicity Results and Algorithmic Applications
- Gowers Uniformity, Influence of Variables, and PCPs
- Growth in groups: ideas and perspectives
- Approximate algebraic structure
- AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
- Quadratic Goldreich-Levin Theorems
- On Certain Sets of Integers
- On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
- An inverse theorem for the Gowers \(U^{s+1}[N\)-norm]
- An inverse theorem for the Gowers \(U^{s+1}[N\)-norm]
- Arithmetic progressions in sumsets
- Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques
- Arithmetic progressions in sumsets
- A new proof of Szemerédi's theorem
This page was built for publication: Finite field models in arithmetic combinatorics -- ten years on