Explicit Methods for Radical Function Fields over Finite Fields

Details Explicit Methods for Radical Function Fields over Finite Fields Explicit Methods for Radical Function Fields over Finite Fields

2009-11-30

arxiv.org/abs/0911.5543v1

Mathematics

Number Theory

29 pages

Scientific paper

We develop explicit formulas and algorithms for arithmetic in radical function fields K/k(x) over finite constant fields. First, we classify which places of k(x) whose local integral bases have an easy monogenic form, and give explicit formulas for these bases. Then, for a fixed place p of k(x), we give formulas for functions whose valuation is zero for all places P | p except one, for which it is one. We extend a result by Q. Wu on a k[x]-basis of its integral closure in K, show how to compute certain Riemann-Roch spaces and how to compute the exact constant field, resulting in explicit formulas for the exact constant field together with easy to evaluate formulas for the genus of K. Finally, we show how to approximate the Euler product to obtain the class number using ideas of R. Scheidler and A. Stein and give an algorithm. We give bounds on the running time for all algorithms.

Affiliated with

Also associated with

No associations

Rating

Explicit Methods for Radical Function Fields over Finite Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Explicit Methods for Radical Function Fields over Finite Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explicit Methods for Radical Function Fields over Finite Fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-148669