An improvement to an algorithm of Belabas, Diaz y Diaz and Friedman

TL;DR

This paper enhances an existing algorithm for determining prime ideals generating a class group under GRH, providing a more efficient method to compute lower bounds for these primes.

Contribution

It introduces a technique to derive lower bounds on prime ideals using Belabas, Diaz y Diaz, and Friedman's main result, improving the efficiency of class group computations.

Findings

New method produces smaller bounds for prime ideals

Algorithmic approach improves efficiency of class group generation

Lower bounds are more optimal than previous results

Abstract

In [BDyDF08] Belabas, Diaz y Diaz and Friedman show a way to determine, assuming the Generalized Riemann Hypothesis, a set of prime ideals that generate the class group of a number field. Their method is efficient because it produces a set of ideals that is smaller than earlier proved results. Here we show how to use their main result to algorithmically produce a bound that is lower than the one they prove.