Under the assumption of the generalized Riemann Hyothesis verifying the class number belongs to NPcapCo-NP
نویسنده
چکیده
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.
منابع مشابه
Some remarks concerning the complexity of computing class groups of quadratic fields
Let O be an order of a quadratic number eld. In this paper we show that under the assumption of the generalized Riemann hypothesis the following decision problems are in NP \ co-NP:
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تاریخ انتشار 1994