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math.NT2010
Sums and Products with Smooth Numbers
William D. Banks, David Covert
We estimate the sizes of the sumset A + A and the productset A A in the special case that A = S (x, y), the set of positive integers n less than or equal to x, free of prim…
math.NT2010★ 1 cited
On group structures realized by elliptic curves over arbitrary finite fields
William D. Banks, Francesco Pappalardi, Igor E. Shparlinski
We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at…