Bent functions on a finite abelian group

We introduce the notion of a bent function on a finite Abelian group which in the case of the elementary Abelian 2-group coincides with the well-known notion of a Boolean bent function. Using methods of the theory of characters and commutative harmonic analysis we obtain a number of properties of bent functions which generalize the corresponding properties of Boolean bent functions. We construct some classes of bent functions.
The last author was supported by the Russian Foundation for Basic Research, grant 96–01–00931.