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Additive Combinatorics
About this Title
Andrew Granville, Université de Montréal, Montréal, QC, Canada, Melvyn B. Nathanson, City University of New York, Lehman College, Bronx, NY and József Solymosi, University of British Columbia, Vancouver, BC, Canada, Editors
Publication: CRM Proceedings and Lecture Notes
Publication Year:
2007; Volume 43
ISBNs: 978-0-8218-4351-2 (print); 978-1-4704-3957-6 (online)
DOI: https://doi.org/10.1090/crmp/043
MathSciNet review: MR2307981
MSC: Primary 11-02; Secondary 11-06, 11P70
ReadershipTable of Contents
Front/Back Matter
Chapters
- An introduction to additive combinatorics
- Elementary additive combinatorics
- Many additive quadruples
- 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