A very special nonexistence theorem for abelian difference sets

摘要

It is wellknown that the technique of character sums together with the tools of algebraic number theory is the adequate method for the study of difference sets in abelian groups, compare for instance Ott [5] or Turyn [6]. In this paper we use this method to prove a new non-existence theorem for certain difference sets in abelian groups of order $ rp^a $ , where $ r neq 2 $ and p are distinct primes.