A343772 Minimal absolute value of negative discriminants of number fields of degree n.

3, 23, 275, 4511, 9747, 184607

Offset

2,1

Comments

Conjecture: A343690(n) < a(n) for n == 0, 1 (mod 4), A343690(n) > a(n) for n == 2, 3 (mod 4).

1257728 <= a(8) <= 4286875.

Links

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

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.

Index entries for sequences related to quadratic fields

Formula

A006557(n) = Min_{A343690(n), a(n)}.

Example

The number field F of degree n whose discriminant is negative and of minimal absolute value:
n = 2, F = Q[x]/(x^2 - x + 1), d = -3;
n = 3, F = Q[x]/(x^3 - x^2 + 1), d = -23;
n = 4, F = Q[x]/(x^4 - x^3 + 2x - 1), d = -275;
n = 5, F = Q[x]/(x^5 - x^3 - 2x^2 + 1), d = -4511;
n = 6, F = Q[x]/(x^6 - x^5 + x^4 - 2x^3 + 4x^2 - 3x + 1), d = -9747;
n = 7, F = Q[x]/(x^7 - x^6 - x^5 + x^4 - x^2 + x + 1), d = -184607.

Crossrefs

Cf. A343690 (the positive discriminant case), A006557 (the overall case).

Sequence in context: A378114 A199544 A302117 * A006555 A357349 A363137

Adjacent sequences: A343769 A343770 A343771 * A343773 A343774 A343775

Keyword

nonn,hard,more

Author

Jianing Song, Apr 29 2021

Status

approved