OFFSET
1,2
COMMENTS
LINKS
LMFDB, Number fields
A. M. Odlyzko, Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: A survey of recent results, Sem. Theorie des Nombres, Bordeaux, 2 (1990), pp. 119-141.
EXAMPLE
The number field F of degree n whose discriminant is positive and of minimal value:
n = 2, F = Q[x]/(x^2 - x - 1), d = 5;
n = 3, F = Q[x]/(x^3 - x^2 - 2x + 1), d = 49;
n = 4, F = Q[x]/(x^4 - x^3 - x^2 + x + 1), d = 117;
n = 5, F = Q[x]/(x^5 - x^3 - x^2 + x + 1), d = 1609;
n = 6, F = Q[x]/(x^6 - 2x^5 + 3x^3 - 2x - 1), d = 28037;
n = 7, F = Q[x]/(x^7 - x^6 + x^5 - x^3 + x^2 - x - 1), d = 612233;
n = 8, F = Q[x]/(x^8 - 2x^7 + 4x^5 - 4x^4 + 3x^2 - 2x + 1), d = 1257728.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jianing Song, Apr 26 2021
STATUS
approved