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Boston, Nigel Bauer, Mark L. 2015-09-28T15:19:31Z 2015-09-28T15:19:31Z 10000-01-01 2001 2001 The second part of the thesis is focussed on developing an explicit arithmetic for the Jacobian of certain cubic superelliptic curves. We restrict our attention to curves of the form y3 = f( x). Assuming that f(x) is monic with no repeated roots and that our field does not have characteristic 3, we are able to show that the Jacobian of this curve is isomorphic to the ideal class group of K[C], the ring of regular functions on C. By exploiting the structure of ideals in K[C] as K[x] modules, we are able to produce a very efficient algorithm for performing group operations in the Jacobian which heuristically should take 46g 2 operations in the finite field K. Made available in DSpace on 2015-09-28T15:19:31Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3023016.pdf: 3528470 bytes, checksum: 229d401710ad3c77f4d321037bcb612b (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88065 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 81 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86784 (MiAaPQ)AAI3023016 eng Mathematics Function Field Arithmetic and Related Algorithms text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.