The construction of the Hilbert genus fields of real cyclic quartic fields

Abstract: Let

p

be a prime number such that

p = 2

or

p e q u i v 1 p m o d 4

. Let

v a r e p s i l o n_{p}

denote the fundamental unit of

m a t h b b Q (s q r t p)

and let

a

be a positive square-free integer. In the present paper, we construct the Hilbert genus field of the real cyclic quartic fields

m a t h b b Q (s q r t a v a r e p s i l o n_{p} s q r t p)

.

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