The cardinality of restricted sumsets.
Estimates for the restricted sumset \(A \widehat + B\) (only distinct summands allowed) are notoriously more difficult to obtain than for the ordinary sumset. The author shows that this difference vanishes if only asymptotic results are sought. The main result asserts that, for arbitrary sets \(A, B\) of integers or residues modulo any integer we have \[ | A \widehat + B | \geq | A+B| (1- c ( \log | A+B| )^{-1/9}) \] with an absolute constant \(c\). The proof is based on a result of the reviewer asserting that a set free of 3-term arithmetic progressions must have a large sumset [Period. Math. Hung. 25, 105--111 (1992; Zbl 0761.11005)].
scientific article; zbMATH DE number 1886707