Fundamental Unit

In a real Quadratic Field, there exists a special Unit known as the fundamental unit such that allunits are given by , for , , , .... The following table gives thefundamental units for the first few real quadratic fields.

2		51
3		53
5		55
6		57
7		58
10		59
11		61
13		62
14		65
15		66
17		67
19		69
21		70
22		71
23		73
26		74
29		77
30		78
31		79
33		82
34		83
35		85
37		86
38		87
39		89
41		91
42		93
43		95
46		97
47

References

Cohn, H. ``Fundamental Units'' and ``Construction of Fundamental Units.'' §6.4 and 6.5 in Advanced Number Theory. New York: Dover, pp. 98-102, and 261-274, 1980.

Weisstein, E. W. ``Class Numbers.'' Mathematica notebook ClassNumbers.m.

• Hyperbolic Spiral Inverse Curve
• Hyperbolic Spiral Roulette
• Hyperbolic Substitution
• Hyperbolic Tangent
• Hyperbolic Tetrahedron
• Hyperbolic Umbilic Catastrophe
• Hyperboloid
• Hyperboloid Embedding
• Hypercomplex Number
• Hypercube
• Hyperdeterminant
• Hyperellipse
• Hyperelliptic Function
• Hyperelliptic Integral
• Hyperfactorial
• Hypergeometric Differential Equation
• Hypergeometric Distribution
• Hypergeometric Function
• Hypergeometric Identity
• Hypergeometric Polynomial
• Hypergeometric Series
• Hypergroup
• Hypermatrix
• Hyperparallel
• Hyperperfect Number