Computing Hilbert Class Polynomials
Abstract
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$ , and we show that all methods have comparable run times.
Domains
Number Theory [math.NT]Origin | Files produced by the author(s) |
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