Exponential sums for nonlinear recurring sequences in residue rings

We prove some new bounds on exponential sums for nonlinear re-curring sequences over residue rings. In addition, we also show similar novelresults when the modulus is almost squarefree, thereby improving the resultsin El-Mahassni, Shparlinski, and Winterhof [11] and El-Mahassni and Winter-hof [13] This is done by using a technique employed by Niederreiter and Win-terhof [26] and through the generalisation of a Lemma found in [11] and [13].Lastly, applications to the distribution of nonlinear congruential pseudoran-dom numbers are also given.