Sums of Dilates in Groups of Prime Order

  • Alain Plagne
  • Published 2011 in Combinatorics, Probability & Computing

Abstract

We obtain a first non-trivial estimate for the sum of dilates problem in the case of groups of prime order, by showing that if t is an integer different from 0, 1 or −1 and if A ⊂ Z/pZ is not too large (with respect to p), then |A+t·A| > (2+θt)|A|−w(t) for some constant w(t) depending only on t and for some explicit real number θt > 0 (except in the case |t… (More)
DOI: 10.1017/S0963548311000447