A006555 Minimal absolute value of discriminants of number fields of degree n with exactly 2 (1 pair of) complex embeddings. (Formerly M3103)

3, 23, 275, 4511, 92779, 2306599

Offset

2,1

Comments

The old definition was "Minimal discriminant of number field of degree n."

From Jianing Song, Apr 29 2021: (Start)

Minimal absolute value of discriminants of number fields with signature r_1 = n - 2, r_2 = 1. For a number field F with degree n, the signature of F is a pair of numbers (r_1, r_2), where r_1 is the number of real embeddings of F, r_2 is half the number of complex embeddings of F. Obviously, we have r_1 + 2*r_2 = n.

This is the second column of A343290, negated. (End)

References

H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 617.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

Example

From Jianing Song, Apr 29 2021: (Start)
The number field F of degree n with exactly 2 complex embeddings (signature r_1 = n - 2, r_2 = 1) whose discriminant is 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 - 2x^4 + 3x^3 - x^2 - 2x + 1), d = -92779;
n = 7, F = Q[x]/(x^7 - 3x^5 - x^4 + x^3 + 3x^2 + x - 1), d = -2306599. (End)

Crossrefs

Cf. A006554, A343290.

Sequence in context: A199544 A302117 A343772 * A357349 A363137 A060090

Adjacent sequences: A006552 A006553 A006554 * A006556 A006557 A006558

Keyword

nonn,hard,more

Author

N. J. A. Sloane.

Extensions

Definition clarified by Jianing Song, Apr 29 2021

Status

approved