The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four
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Citations
Cites
�ber die Gleichverteilung von Zahlen mod. Eins
Weyl, H. (1916) · Mathematische Annalen · doi:10.1007/bf01475864 · Cited by 1,263
Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions
Furstenberg, H. (1977) · Journal d Analyse Mathématique · doi:10.1007/bf02813304 · Cited by 804
Roth, K. F. (1953) · Journal of the London Mathematical Society · doi:10.1112/jlms/s1-28.1.104 · Cited by 586
Foundations of a Structural Theory of Set Addition
Freiman, G. (2007) · Translations of Mathematical Monographs · doi:10.1090/mmono/037 · Cited by 347
Erdös, P., & Turán, P. (1936) · Journal of the London Mathematical Society · doi:10.1112/jlms/s1-11.4.261 · Cited by 310
Integer Sets Containing No Arithmetic Progressions
Heath-Brown, D. R. (1987) · Journal of the London Mathematical Society · doi:10.1112/jlms/s2-35.3.385 · Cited by 161
On sets of integers containing no four elements in arithmetic progression
Szemerédi, E. (1969) · Acta Mathematica Academiae Scientiarum Hungaricae · doi:10.1007/bf01894569 · Cited by 159
Integer sets containing no arithmetic progressions
Szemerédi, E. (1990) · Acta Mathematica Academiae Scientiarum Hungaricae · doi:10.1007/bf01903717 · Cited by 123
Cited by
The primes contain arbitrarily long arithmetic progressions
Green, B., & Tao, T. (2008) · Annals of Mathematics · doi:10.4007/annals.2008.167.481 · Cited by 803
New applications of the polynomial method: The cap set conjecture and beyond
Grochow, J. (2018) · Bulletin of the American Mathematical Society · doi:10.1090/bull/1648 · Cited by 16
“Gowers observed [62, p. 273] that if the upper bound on r3(Z/NZ) could be improved from its current record of N(log logN)4/ logN [16] to N log logN/ logN , it would give an alternative proof of Roth’s theorem in the primes (a theorem due to Green [65] with improved bounds by Helfgott and de Roton [75]).”
Method
Metadata
- Authors
- Gowers, W. T.
- Venue
- Geometric And Functional Analysis
- Published
- 1998-07-01
- Volume
- 8
- Issue
- 3
- Pages
- 529-551
- ISSN
- 1016-443X (ISSN-L)
- 1420-8970
- OpenAlex
- W2342433841
- Cited by
- 417
- References
- 8
- FWCI
- 11.21
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four. https://app.cochat.ai/papers/10.1007/s000390050065
- The paper
- Gowers, W. T. (1998). A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four. Geometric And Functional Analysis. https://doi.org/10.1007/s000390050065
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
