Cyclic-sixteen class fields for 𝑄((-𝑝)^{1/2}) by modular arithmetic

Abstract

Numerical experiments result in the construction of cyclic-sixteen class fields for Q ( − p ) 1 / 2 {\mathbf {Q}}{( - p)^{1/2}} , p prime > 2000 > 2000 , by radicals involving quadratic and biquadratic parameters. These fields are characterized by rational factorization properties modulo a variable prime; but it suffices to use only three primes selected and checked by computer to verify the class field, if earlier work (jointly with Cooke) on the cyclic-eight class field is utilized.