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Additive Combinatorics
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  • Cited by 237
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Shkredov, Ilya 2019. Some remarks on the asymmetric sum-product phenomenon. Moscow Journal of Combinatorics and Number Theory, Vol. 8, Issue. 1, p. 15.

    Hough, Robert 2018. The local limit theorem on nilpotent Lie groups. Probability Theory and Related Fields,

    Liu, Zhengwei and Wu, Jinsong 2018. Extremal pairs of Young’s inequality for Kac algebras. Pacific Journal of Mathematics, Vol. 295, Issue. 1, p. 103.

    Roginskaya, M. M. and Shulman, V. S. 2018. On Minkowski Sums of Many Small Sets. Functional Analysis and Its Applications, Vol. 52, Issue. 3, p. 232.

    Chi, Zhiyi 2018. On a Multivariate Strong Renewal Theorem. Journal of Theoretical Probability, Vol. 31, Issue. 3, p. 1235.

    Götze, Friedrich and Zaitsev, Andrei Yu. 2018. New applications of Arak’s inequalities to the Littlewood–Offord problem. European Journal of Mathematics, Vol. 4, Issue. 2, p. 639.

    Shkredov, I. D. 2018. Differences of subgroups in subgroups. International Journal of Number Theory, Vol. 14, Issue. 04, p. 1111.

    Benhamouda, Fabrice Degwekar, Akshay Ishai, Yuval and Rabin, Tal 2018. Advances in Cryptology – CRYPTO 2018. Vol. 10991, Issue. , p. 531.

    Габдуллин, Михаил Рашидович and Gabdullin, Mikhail Rashidovich 2018. О подмножествах $\mathbb{Z}_m$, разность которых не содержит квадратов. Математический сборник, Vol. 209, Issue. 11, p. 60.

    Roche-Newton, Oliver Ruzsa, Imre Z. Shen, Chun-Yen and Shkredov, Ilya D. 2018. On the size of the set AA+A. Journal of the London Mathematical Society,

    Shkredov, I. D. 2018. An application of the sum-product phenomenon to sets avoiding several linear equations. Sbornik: Mathematics, Vol. 209, Issue. 4, p. 580.

    Madiman, Mokshay and Kontoyiannis, Ioannis 2018. Entropy Bounds on Abelian Groups and the Ruzsa Divergence. IEEE Transactions on Information Theory, Vol. 64, Issue. 1, p. 77.

    Tran, Tuan 2018. On the structure of large sum-free sets of integers. Israel Journal of Mathematics, Vol. 228, Issue. 1, p. 249.

    Иосевич, Александр Iosevich, Alexander Роше-Ньютон, Оливер Roche-Newton, Oliver Руднев, Михаил Константинович and Rudnev, Mikhail Konstantinovich 2018. О дискретных значениях билинейных форм. Математический сборник, Vol. 209, Issue. 10, p. 71.

    Candela, Pablo and Szegedy, Balázs 2018. A continuous model for systems of complexity 2 on simple abelian groups. Journal d'Analyse Mathématique, Vol. 135, Issue. 2, p. 437.

    Lachmann, Thomas and Technau, Niclas 2018. On exceptional sets in the metric Poissonian pair correlations problem. Monatshefte für Mathematik,

    Рогинская, Мария Мартыновна Roginskaya, Maria Martinovna Шульман, Виктор Семенович and Shul'man, Viktor Semenovich 2018. О суммах по Минковскому большого числа малых слагаемых. Функциональный анализ и его приложения, Vol. 52, Issue. 3, p. 88.

    Bystrzycki, Rafał 2018. Number-Theoretic Methods in Cryptology. Vol. 10737, Issue. , p. 178.

    SHAKAN, GEORGE 2018. On higher energy decompositions and the sum–product phenomenon. Mathematical Proceedings of the Cambridge Philosophical Society, p. 1.

    Huicochea, Mario 2018. A proof of a conjecture of Lev. International Journal of Number Theory, Vol. 14, Issue. 10, p. 2583.


Book description

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.


'The book under review is a vital contribution to the literature, and it has already become required reading for a new generation of students as well as for experts in adjacent areas looking to learn about additive combinatorics. … This was very much a book that needed to be written at the time it was, and the authors are to be highly commended for having done so in such an effective way.'

Source: Bulletin of the American Mathematical Society

'The book gathers diverse important techniques used in additive combinatorics, and its main advantage is that it is written in a very readable and easy to understand style. The authors try very successfully to develop all the necessary background material … [which] makes the book useful not only to graduate students, but also to researchers who are interested to learn more about the variety of diverse tools and ideas applied in this fascinating subject.'

Source: Zentralblatt MATH

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