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[parent] table of some fundamental units (Result)

Below, we tabulate the fundamental units $ \eta$ of first real quadratic fields $ \mathbb{Q}(\sqrt{d})$; the number $ \omega$ is $ \displaystyle\frac{1\!+\!\sqrt{d}}{2}$ for $ d \equiv 1 \pmod{4}$ and $ \sqrt{d}$ for $ d \not\equiv 1 \pmod{4}$.

$ d$ $ \eta$ $ d$ $ \eta$
$ 2$ $ 1+\omega$ $ 47$ $ 48+7\omega$
$ 3$ $ 2+\omega$ $ 51$ $ 50+7\omega$
$ 5$ $ \omega$ $ 53$ $ 3+\omega$
$ 6$ $ 5+2\omega$ $ 55$ $ 89+12\omega$
$ 7$ $ 8+3\omega$ $ 57$ $ 131+40\omega$
$ 10$ $ 3+\omega$ $ 58$ $ 99+13\omega$
$ 11$ $ 10+3\omega$ $ 59$ $ 530+69\omega$
$ 13$ $ 1+\omega$ $ 61$ $ 17+5\omega$
$ 14$ $ 15+4\omega$ $ 62$ $ 63+8\omega$
$ 15$ $ 4+\omega$ $ 65$ $ 7+2\omega$
$ 17$ $ 3+2\omega$ $ 66$ $ 65+8\omega$
$ 19$ $ 170+39\omega$ $ 67$ $ 48842+5967\omega$
$ 21$ $ 2+\omega$ $ 69$ $ 11+3\omega$
$ 22$ $ 197+42\omega$ $ 70$ $ 251+30\omega$
$ 23$ $ 24+5\omega$ $ 71$ $ 3480+413\omega$
$ 26$ $ 5+\omega$ $ 73$ $ 943+250\omega$
$ 29$ $ 2+\omega$ $ 74$ $ 43+5\omega$
$ 30$ $ 11+2\omega$ $ 77$ $ 4+\omega$
$ 31$ $ 1520+273\omega$ $ 78$ $ 53+6\omega$
$ 33$ $ 19+8\omega$ 79 $ 80+9\omega$
$ 34$ $ 35+6\omega$ $ 82$ $ 9+\omega$
$ 35$ $ 6+\omega$ $ 83$ $ 82+9\omega$
$ 37$ $ 5+2\omega$ $ 85$ $ 4+\omega$
$ 38$ $ 37+6\omega$ $ 86$ $ 10405+1122\omega$
$ 39$ $ 25+4\omega$ $ 87$ $ 28+3\omega$
$ 41$ $ 27+10\omega$ $ 89$ $ 447+106\omega$
$ 42$ $ 13+2\omega$ $ 91$ $ 1574+165\omega$
$ 43$ $ 3482+531\omega$ $ 93$ $ 13+3\omega$
$ 46$ $ 24335+3588\omega$ $ 94$ $ 2143295+221064\omega$

Bibliography

1
S. BOREWICZ & I. SAFAREVIC: Zahlentheorie. Birkhäuser Verlag. Basel und Stuttgart (1966).



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See Also: units of quadratic fields, quadratic field, integral basis of quadratic field, algebraic number theory


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Cross-references: real quadratic fields, fundamental units

This is version 6 of table of some fundamental units, born on 2008-04-07, modified 2008-04-08.
Object id is 10486, canonical name is SomethingRelatedToFundamentalUnits.
Accessed 194 times total.

Classification:
AMS MSC: 11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers)
 11R11 (Number theory :: Algebraic number theory: global fields :: Quadratic extensions)
 11R27 (Number theory :: Algebraic number theory: global fields :: Units and factorization)
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