Clifford Reiter, Effective Lower Bounds on Large Fundamental Units of Real Quadratic Fields, Osaka Journal of Mathematics, 22 4 (1985), 755-765.

This paper constructs explicit bounds on Yamamoto's theorem on the growth of the fundamental unit for families of quadratic extensions where a fixed set of primes are known to be principal. In particular, log(ed) > C (log d)n+1 where ed is the fundamental unit and n is the number of principal ideals. Furthermore, the monomial norm equation, Ai(x)2-Bi(x)2D(x)=cixe_i is introduced and studied. It is used to create many families (each based upon factorizations of xn-1) with two principal ideals.

See Also: · A motivating reference: Y. Yamamoto, Real Quadratic Fields with large fundamental units, Osaka Journal of Mathematics, 8 (1971), 261-270. · Used experiments based on computations done using the note: [Abstract ci_1988]