A072104 Smallest absolute value of discriminant of a real (not necessarily totally real) algebraic number field of degree n.

5, 23, 275, 1609, 28037, 184607

Offset

2,1

Comments

These values are important in Diophantine approximation theory and in the geometry of numbers. Krass (1985) proved that the n-dimensional simultaneous Diophantine approximation constant, gamma_n, must satisfy gamma_n >= (16/9)^floor(n/4) / sqrt(a_(n+1)). See web site for a continuation of probable values.

References

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 174-179.

Links

Table of n, a(n) for n=2..7.

Gerhard Niklasch, Smallest Discriminants of Number Fields

Crossrefs

Sequence in context: A361362 A197936 A198029 * A086797 A023275 A018899

Adjacent sequences: A072101 A072102 A072103 * A072105 A072106 A072107

Keyword

hard,nonn

Author

Robert G. Wilson v, Jun 18 2002

Status

approved