Finding arithmetic progressions in dense sets of integers

Дата публикации: 06-10-2026 14:16:00

Sarah Peluse

Bull. Amer. Math. Soc. 63 (), 531-557.

Abstract, references and article information

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Bull. Amer. Math. Soc. 63 (2026), 531-557
DOI: https://doi.org/10.1090/bull/1883
Published electronically: August 12, 2026
Bull. Amer. Math. Soc. 63 (2026), 559-636
DOI: https://doi.org/10.1090/bull/1890
Published electronically: August 12, 2026
Bull. Amer. Math. Soc. 63 (2026), 637-684
DOI: https://doi.org/10.1090/bull/1908
Published electronically: August 13, 2026
- Bull. Amer. Math. Soc. 63 (2026), 685-691
  DOI: https://doi.org/10.1090/bull/1905
  Published electronically: August 12, 2026

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Bull. Amer. Math. Soc. 63 (2026), 531-557
DOI: https://doi.org/10.1090/bull/1883
Published electronically: August 12, 2026
Bull. Amer. Math. Soc. 63 (2026), 559-636
DOI: https://doi.org/10.1090/bull/1890
Published electronically: August 12, 2026
Bull. Amer. Math. Soc. 63 (2026), 637-684
DOI: https://doi.org/10.1090/bull/1908
Published electronically: August 13, 2026
- Bull. Amer. Math. Soc. 63 (2026), 685-691
  DOI: https://doi.org/10.1090/bull/1905
  Published electronically: August 12, 2026

Bull. Amer. Math. Soc. 63 (2026), 531-557

DOI: https://doi.org/10.1090/bull/1883

Published electronically: August 12, 2026

Abstract

One of the central problems in additive combinatorics is to determine how large a subset of the first $N$ integers can be before it is forced to contain $k$ elements forming an arithmetic progression. Around twenty-five years ago, Gowers proved the first reasonable upper bounds in this problem for progressions of length four and longer. In this work, Gowers initiated the study of “higher-order Fourier analysis,” which has developed over the past couple of decades into a rich theory with numerous other combinatorial applications. I will report on some very recent progress in higher-order Fourier analysis and how it has led to the first ever quantitative improvement on Gowers’s upper bounds when $k\geq 5$.

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Sarah Peluse
Affiliation: Department of Mathematics, Stanford University, 450 Jane Stanford Way, Building 380, Stanford, California 94305
MR Author ID: 1035915
Email: [email protected]
Published electronically: August 12, 2026
© Copyright 2026 American Mathematical Society
Journal: Bull. Amer. Math. Soc. 63 (2026), 531-557
MSC (2020): Primary 11B30
DOI: https://doi.org/10.1090/bull/1883

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Finding arithmetic progressions in dense sets of integers

Дата публикации: 06-10-2026 14:16:00

Основное содержимое страницы с новостью.

Схожие новости