Sumsets of multiplicative subgroups in Z_p

Combinatorics Seminar
Friday, March 8, 2013 - 15:00
1 hour (actually 50 minutes)
Skiles 005
Kansas State University
Let A be a multiplicative subgroup of Z_p^*. Define the k-fold sumset of A to be kA={x_1+...+x_k:x_1,...,x_k in A}. Recently, Shkredov has shown that |2A| >> |A|^(8/5-\epsilon) for |A| < p^(9/17). In this talk we will discuss extending this result to hold for |A| < p^(5/9). In addition, we will show that 6A contains Z_p^* for |A| > p^(33/71 +\epsilon).