SHORT PROOFS USING COMPACT REPRESENTATIONS OF ALGEBRAIC-INTEGERS

We show that under the assumption of a certain generalized Riemann hypothesis the problem of verifying the value of the class number of an arbitrary algebraic number field of arbitrary degree belongs to the complexity class NP. In order to prove this result we introduce compact representations of algebraic integers which allows us to represent a system of fundamental units by (log(2)(Delta))(O(1)) bits. (C) 1995 Academic Press, Inc.