On the quartic residue symbol of totally positive quadratic units (Q1083477)

Let m be squarefree positive integer and \(\epsilon_ m\) \((>1)\) the fundamental unit of the real quadratic field \({\mathbb{Q}}(\sqrt{m})\). For a rational prime p satisfying \[ (\frac{- 1}{p})=(\frac{m}{p})=(\frac{\epsilon_ m}{p})=1, \] the biquadratic symbol \((\frac{\epsilon_ m}{p})_ 4\) is defined. The author evaluates this symbol in the following cases: \[ m=qq': q\equiv 3,5\quad (\bmod 8),\;q'\equiv 3\;(\bmod 4),\;(\frac{q}{q'})=-1,\;m=2q: q\equiv 3\;(\bmod 8),\;m=q: q\equiv 3,7,11\;(\bmod 16), \] where q and q' denote prime numbers.