Quantitative sum product estimates on different sets.
Rainbow 3-term arithmetic progressions.
Remarks on number theory III. On addition chains
Remarks on systems of congruence classes
Representation functions, Sidon sets and bases
Representation of finite abelian group elements by subsequence sums
Let be a finite and nontrivial abelian group with . A conjecture of Hamidoune says that if is a sequence of integers, all but at most one relatively prime to , and is a sequence over with , the maximum multiplicity of at most , and , then there exists a nontrivial subgroup such that every element can be represented as a weighted subsequence sum of the form , with a subsequence of . We give two examples showing this does not hold in general, and characterize the counterexamples...
Restricted set addition in Abelian groups: results and conjectures
We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of Erdős-Heilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed.The paper assumes no expertise from the reader and can serve as an introduction to the subject.
Restricted set addition in groups. II: A generalization of the Erdős-Heilbronn conjecture.
Restricted sums in a field
Restricted sumsets in finite vector spaces: the case .
Sequences with bounded l.c.m. of each pair of terms
Sequences with bounded l.c.m. of each pair of terms II
Sequences with bounded l.c.m. of each pair of terms, III
Sets of integers and quasi-integers with pairwise common divisor
Sets of integers with pairwise common divisor and a factor from a specified set of primes
Sets with more sums than differences.
Short character sums with Fermat quotients
Slightly improved sum-product estimates in fields of prime order
Small maximal sum-free sets.
Small-sum pairs in abelian groups
Let be an abelian group and two subsets of equal size such that and both have size . Answering a question of Bihani and Jin, we prove that if is aperiodic or if there exist elements and such that has a unique expression as an element of and has a unique expression as an element of , then is a translate of . We also give an explicit description of the various counterexamples which arise when neither condition holds.