Sums of dilates in groups of prime order

Original · EN

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 ⊂ is not too large (with respect to p), then |+t· |>(2+ ϑₜ)||-w(t) for some constant w(t) depending only on t and for some explicit real number ϑₜ >0 (except in the case |t|=3). In the important case |t|=2, we may for instance take ϑ₂=0.08.