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table of some fundamental units
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(Result)
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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 |
$80+9\omega$ |
| $34$ |
$35+6\omega$ |
$82$ |
$9+\omega$ |
| $35$ |
$6+\omega$ |
$83$ |
$82+9\omega$ |
| $37$ |
$5+2\omega$ |
$85$ |
$4+\omega$ |
| $38$ |
$37+6\omega$ |
$86$ |
$10405+1122\omega$ |
| $39$ |
$25+4\omega$ |
$87$ |
$28+3\omega$ |
| $41$ |
$27+10\omega$ |
$89$ |
$447+106\omega$ |
| $42$ |
$13+2\omega$ |
$91$ |
$1574+165\omega$ |
| $43$ |
$3482+531\omega$ |
$93$ |
$13+3\omega$ |
| $46$ |
$24335+3588\omega$ |
$94$ |
$2143295+221064\omega$ |
- 1
- S. BOREWICZ & I. SAFAREVIC: Zahlentheorie. Birkhäuser Verlag. Basel und Stuttgart (1966).
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"table of some fundamental units" is owned by pahio.
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Cross-references: number, real quadratic fields, fundamental units
There is 1 reference to this entry.
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 616 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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Pending Errata and Addenda
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