h-Fold Sums from a Set with Few Products

Before we state our main theorems, we begin with some notation: given a finite subset A of some commutative ring, we let A + A denote the set of sums a + b, where a, b ∈ A; and, we let A.A denote the set of products ab, a, b ∈ A. When three or more sums or products are used, we let kA denote the k-fold sumset A+A+ · · ·+A, and let A denote the k-fold product set A.A...A. Lastly, by d ∗ A we mea...

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2 00 9 k - fold sums from a set with few products Dedicated to the memory of György Elekes Ernie

Before we state our main theorems, we begin with some notation: given a finite subset A of some commutative ring, we let A + A denote the set of sums a + b, where a, b ∈ A; and, we let A.A denote the set of products ab, a, b ∈ A. When three or more sums or products are used, we let kA denote the k-fold sumset A+A+ · · ·+A, and let A denote the k-fold product set A.A...A. Lastly, by d ∗ A we mea...

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2 00 9 k - fold sums from a set with few products Dedicated to the memory of György Elekes

Before we state our main theorems, we begin with some notation: given a finite subset A of some commutative ring, we let A + A denote the set of sums a + b, where a, b ∈ A; and, we let A.A denote the set of products ab, a, b ∈ A. When three or more sums or products are used, we let kA denote the k-fold sumset A+A+ · · ·+A, and let A denote the k-fold product set A.A...A. Lastly, by d ∗ A we mea...

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A pr 2 00 9 k - fold sums from a set with few products Dedicated to the memory of György Elekes Ernie Croot

Before we state our main theorems, we begin with some notation: given a finite subset A of some commutative ring, we let A + A denote the set of sums a + b, where a, b ∈ A; and, we let A.A denote the set of products ab, a, b ∈ A. When three or more sums or products are used, we let kA denote the k-fold sumset A+A+ · · ·+A, and let A denote the k-fold product set A.A...A. Lastly, by d ∗ A we mea...

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2 00 9 k - fold sums from a set with few products Dedicated to the memory of György Elekes Ernie Croot Derrick Hart

Before we state our main theorems, we begin with some notation: given a finite subset A of some commutative ring, we let A + A denote the set of sums a + b, where a, b ∈ A; and, we let A.A denote the set of products ab, a, b ∈ A. When three or more sums or products are used, we let kA denote the k-fold sumset A+A+ · · ·+A, and let A denote the k-fold product set A.A...A. Lastly, by d ∗ A we mea...

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h-Fold Sums from a Set with Few Products

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