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Title:Function Field Arithmetic and Related Algorithms
Author(s):Bauer, Mark L.
Doctoral Committee Chair(s):Boston, Nigel
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract: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.
Issue Date:2001
Type:Text
Language:English
Description:81 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.
URI:http://hdl.handle.net/2142/86784
Other Identifier(s):(MiAaPQ)AAI3023016
Date Available in IDEALS:2015-09-28
Date Deposited:2001


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