摘要 : In order to study the density of the set of positive integers d for which the negative Pell equation x(2)-dy(2)=-1 is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadra... 展开 In order to study the density of the set of positive integers d for which the negative Pell equation x(2)-dy(2)=-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 for the density heuristics for the negative Pell equation proposed by the second author. In particular, an irrational proportion P=1-Pi(j greater than or equal to 1 odd)(1-2(-j))approximate to.58 of the real quadratic fields without discriminantal prime divisors congruent to 3 mod 4 should have a fundamental unit of norm -1. [References: 12] 收起