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Edited by: Andrew Granville Université de Montréal, Montréal, QC, Canada
Melvyn B. Nathanson City University of New York, Lehman College, Bronx, NY
József Solymosi University of British Columbia, Vancouver, BC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Available Formats:
Softcover ISBN: 978-0-8218-4351-2
Product Code: CRMP/43
List Price: $112.00 MAA Member Price:$100.80
AMS Member Price: $89.60 Electronic ISBN: 978-1-4704-3957-6 Product Code: CRMP/43.E List Price:$105.00
MAA Member Price: $94.50 AMS Member Price:$84.00
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List Price: $168.00 MAA Member Price:$151.20
AMS Member Price: $134.40 Click above image for expanded view Additive Combinatorics Edited by: Andrew Granville Université de Montréal, Montréal, QC, Canada Melvyn B. Nathanson City University of New York, Lehman College, Bronx, NY József Solymosi University of British Columbia, Vancouver, BC, Canada A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats:  Softcover ISBN: 978-0-8218-4351-2 Product Code: CRMP/43  List Price:$112.00 MAA Member Price: $100.80 AMS Member Price:$89.60
 Electronic ISBN: 978-1-4704-3957-6 Product Code: CRMP/43.E
 List Price: $105.00 MAA Member Price:$94.50 AMS Member Price: $84.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$168.00 MAA Member Price: $151.20 AMS Member Price:$134.40
• Book Details

CRM Proceedings & Lecture Notes
Volume: 432007; 335 pp
MSC: Primary 11; Secondary 05; 42; 28; 37;

One of the most active areas in mathematics today is the rapidly emerging new topic of “additive combinatorics”. Building on Gowers' use of the Freiman–Ruzsa theorem in harmonic analysis (in particular, his proof of Szemerédi's theorem), Green and Tao famously proved that there are arbitrarily long arithmetic progressions of primes, and Bourgain and his co-authors have given non-trivial estimates for hitherto untouchably short exponential sums. There are further important consequences in group theory and in complexity theory and compelling questions in ergodic theory, discrete geometry and many other disciplines. The basis of the subject is not too difficult: it can be best described as the theory of adding together sets of numbers; in particular, understanding the structure of the two original sets if their sum is small. This book brings together key researchers from all of these different areas, sharing their insights in articles meant to inspire mathematicians coming from all sorts of different backgrounds.

Undergraduates, graduate students, and research mathematicians interested in additive combinatorics.

• Chapters
• An introduction to additive combinatorics
• Elementary additive combinatorics
• An old new proof of Roth’s theorem
• Bounds on exponential sums over small multiplicative subgroups
• Montréal notes on quadratic Fourier analysis
• Ergodic methods in additive combinatorics
• The ergodic and combinatorial approaches to Szemerédi’s theorem
• Cardinality questions about sumsets
• Open problems in additive combinatorics
• Some problems related to sum-product theorems
• Lattice points on circles, squares in arithmetic progressions and sumsets of squares
• Problems in additive number theory. I
• Double and triple sums modulo a prime
• Additive properties of product sets in fields of prime order
• Many sets have more sums than differences
• Davenport’s constant for groups of the form $\mathbb {Z}_3\oplus \mathbb {Z}_3\oplus \mathbb {Z}_{3d}$
• Some combinatorial group invariants and their generalizations with weights
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 432007; 335 pp
MSC: Primary 11; Secondary 05; 42; 28; 37;

One of the most active areas in mathematics today is the rapidly emerging new topic of “additive combinatorics”. Building on Gowers' use of the Freiman–Ruzsa theorem in harmonic analysis (in particular, his proof of Szemerédi's theorem), Green and Tao famously proved that there are arbitrarily long arithmetic progressions of primes, and Bourgain and his co-authors have given non-trivial estimates for hitherto untouchably short exponential sums. There are further important consequences in group theory and in complexity theory and compelling questions in ergodic theory, discrete geometry and many other disciplines. The basis of the subject is not too difficult: it can be best described as the theory of adding together sets of numbers; in particular, understanding the structure of the two original sets if their sum is small. This book brings together key researchers from all of these different areas, sharing their insights in articles meant to inspire mathematicians coming from all sorts of different backgrounds.

Undergraduates, graduate students, and research mathematicians interested in additive combinatorics.

• Chapters
• An introduction to additive combinatorics
• Elementary additive combinatorics
• An old new proof of Roth’s theorem
• Bounds on exponential sums over small multiplicative subgroups
• Montréal notes on quadratic Fourier analysis
• Ergodic methods in additive combinatorics
• The ergodic and combinatorial approaches to Szemerédi’s theorem
• Cardinality questions about sumsets
• Open problems in additive combinatorics
• Some problems related to sum-product theorems
• Lattice points on circles, squares in arithmetic progressions and sumsets of squares
• Problems in additive number theory. I
• Double and triple sums modulo a prime
• Additive properties of product sets in fields of prime order
• Many sets have more sums than differences
• Davenport’s constant for groups of the form $\mathbb {Z}_3\oplus \mathbb {Z}_3\oplus \mathbb {Z}_{3d}$
• Some combinatorial group invariants and their generalizations with weights
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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