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Sum and product of different sets
Let A and B be two finite sets of numbers.
The sum set and the product set of A, B are A + B = {a + b : a in A, b in B}, and
AB = {ab : a in A, b in B}. $ We prove that A+B is as large as
possible when AA is not too big. Similarly, AB is large when
A+A is not too big. The methods rely on the Lambda_p constant
of A, bound on the number of factorizations in a generalized
progression containing A, and the subspace theorem
Double Character Sums over Subgroups and Intervals
We estimate double sums with a multiplicative character
modulo where and is a subgroup of order
of the multiplicative group of the finite field of elements. A nontrivial
upper bound on can be derived from the Burgess bound if and from some standard elementary arguments if , where is arbitrary. We obtain a
nontrivial estimate in a wider range of parameters and . We also
estimate double sums and give an application to primitive
roots modulo with non-zero binary digits
Postulation of canonical curves in â„™ 3
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46228/1/208_2005_Article_BF01458014.pd
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