Under the assumption of the generalized Riemann Hyothesis verifying the class number belongs to NPcapCo-NP

  title={Under the assumption of the generalized Riemann Hyothesis verifying the class number belongs to NPcapCo-NP},
  author={Christoph Thiel},
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 eld F of arbitrary degree belongs to the complexity class NP \ co ?NP. In order to prove this result we introduce a compact representation of algebraic integers which allows us to represent a system of fundamental units by (2 + log 2 ()) O(1) bits, where is the discriminant of F. 

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