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We discuss the problem of constructing a small subset of a finite field containing primitive elements of the field. Given a finite field, F q n , small q and large n, we show that the set of all low degree polynomials contains the expected number of primitive elements. The main theorem we prove is a bound for character sums over short intervals in function… (More)

A theorem of Glasner says that if X is an infinite subset of the torus T, then for any > 0, there exists an integer n such that the dilation nX = {nx : x ∈ T} is-dense (i.e, it intersects any interval of length 2 in T). Alon and Peres provided a general framework for this problem, and showed quantitatively that one can restrict the dilation to be of the… (More)

We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions (GAPs), and Bohr sets, each of which generalizes affine sources. We give an explicit extractor for additive sources with… (More)

We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions (GAPs), and Bohr sets, each of which generalizes affine sources. We give an explicit extractor for additive sources with… (More)

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