Minimal Polynomials of Singular Moduli

Details Minimal Polynomials of Singular Moduli Minimal Polynomials of Singular Moduli

2011-01-07

arxiv.org/abs/1101.1530v1

Mathematics

Number Theory

9 pages, 2 figures

Scientific paper

Given a properly normalized parametrization of a genus-0 modular curve, the complex multiplication points map to algebraic numbers called singular moduli. In the classical case, the maps can be given analytically. However, in the Shimura curve cases, no such analytical expansion is possible. Fortunately, in both cases there are known algorithms for algebraically computing the rational norms of the singular moduli. We demonstrate a method of using these norm algorithms to algebraically determine the minimal polynomial of the singular moduli below a discriminant threshold. We then use these minimal polynomials to compute the algebraic $abc$-ratios for the singular moduli.

Affiliated with

Also associated with

No associations

Rating

Minimal Polynomials of Singular Moduli 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 Minimal Polynomials of Singular Moduli, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal Polynomials of Singular Moduli will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-8343