Advanced Search

Various techniques are presented for constructing $\Lambda$ (p) sets which are not $\Lambda (p+ϵ)$ for all $ϵ\>0$. The main result is that there is a $\Lambda$ (4) set in the dual of any compact abelian group which is not $\Lambda (4+ϵ)$ for all $ϵ\>0$. Along the way to proving this, new constructions are given in dual groups in which constructions were already known of $\Lambda$ (p) not $\Lambda (p+ϵ)$ sets, for certain values of $p$. The main new constructions in specific dual groups are: – there is a $\Lambda$ (2k) set which is not $\Lambda (2k+ϵ)$ in $\mathbf{Z}\left(2\right)\oplus \mathbf{Z}\left(2\right)\oplus \cdots$ for all $2\le k$, $k\in \mathbf{N}$ and $ϵ\>0$, and in...