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

Cohn, Harvey

doi:10.1090/S0025-5718-1979-0537976-5

Cyclic-sixteen class fields for $\textbf {Q}((-p)^{1/2})$ by modular arithmetic
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Math. Comp. 33 (1979), 1307-1316 Request permission

Abstract:

Numerical experiments result in the construction of cyclic-sixteen class fields for ${\mathbf {Q}}{( - p)^{1/2}}$, p prime $< 2000$, 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.

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