Decision Problems in Quadratic Function Fields of High Genus

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Decision Problems in Quadratic Function Fields of High Genus
This paper provides verification procedures for a number of decision problems in quadratic function fields of odd characteristic, thereby establishing membership of these problems in both NP and co-NP. The problems include determining the ideal and divisor class numbers of the field, the regulator of the field (in the real case), a generating system of the ideal class group, a basis of the ideal class group, the pricipality of an ideal, the equivalence of two ideals, the discrete logarithm of an ideal class with respect to another ideal class, and the order of a class in the ideal class group. While several of these problems belong to the aforementioned complexity classes unconditionally, others require a certain assumption to ensure that the verification procedures can be done in polynomial time; so far, this assumption has only been verified for fields of high genus.
Renate Scheidler
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where JC
Authors Renate Scheidler
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