Construction of hyperelliptic function fields of high three-rank

Abstract

We present several explicit constructions of hyperelliptic function fields whose Jacobian or ideal class group has large 3-rank. Our focus is on finding examples for which the genus and the base field are as small as possible. Most of our methods are adapted from analogous techniques used for generating quadratic number fields whose ideal class groups have… (More)
DOI: 10.1090/S0025-5718-07-02001-7

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@article{Bauer2008ConstructionOH, title={Construction of hyperelliptic function fields of high three-rank}, author={M. Bauer and Michael J. Jacobson and Y. Lee and Renate Scheidler}, journal={Math. Comput.}, year={2008}, volume={77}, pages={503-530} }