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2004

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In this paper, we discuss the properties of curves of the form y 3 = f (x) over a given field K of characteristic different from 3. If f (x) satisfies certain properties, then the Jacobian of such a curve is isomorphic to the ideal class group of the maximal order in the corresponding function field. We seek to make this connection concrete and then use it… (More)

The best practical algorithm for class group computations in imaginary quadratic number fields (such as group structure, class number , discrete logarithm computations) is a variant of the quadratic sieve factoring algorithm. Paradoxical as it sounds, the principles of the number field sieve, in a strict sense, could not be applied to number field… (More)

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