No abstract

In this paper, we use the Lagrange neighbour and our equivalence theorem for primitive ideals to obtain lower bounds which are sharper than those given in the literature for class numbers of real quadratic fields in general, but applied to greatest advantage when d is of ERD type.

The aim of this paper is to give lower bounds for class numbers of real quadratic fields in terms of the divisor function, and to develop useful criteria for reduced ideals in terms of both continued fractions and the solvability of diophantine equations, which we then relate back to the aforementioned class number bounds.