Density computations for real quadratic units

@article{Bosma1996DensityCF,
  title={Density computations for real quadratic units},
  author={Wieb Bosma and Peter Stevenhagen},
  journal={Math. Comput.},
  year={1996},
  volume={65},
  pages={1327-1337}
}
In order to study the density of the set of positive integers d for which the negative Pell equation x2 − dy2 = −1 is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadratic orders. A fast algorithm that computes 2-class groups rather than units is used. It is random polynomial-time in log d as the factorization of d is a natural part of the input for the values of d we encounter. The data obtained provide convincing numerical evidence… CONTINUE READING

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