%I M3103 #38 May 17 2021 02:02:51
%S 3,23,275,4511,92779,2306599
%N Minimal absolute value of discriminants of number fields of degree n with exactly 2 (1 pair of) complex embeddings.
%C The old definition was "Minimal discriminant of number field of degree n."
%C From _Jianing Song_, Apr 29 2021: (Start)
%C 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.
%C This is the second column of A343290, negated. (End)
%D H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 617.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H LMFDB, <a href="https://www.lmfdb.org/NumberField">Number fields</a>
%H A. M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/zeta.html">Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: A survey of recent results</a>, Sem. Theorie des Nombres, Bordeaux, 2 (1990), pp. 119-141.
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%e From _Jianing Song_, Apr 29 2021: (Start)
%e 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:
%e n = 2, F = Q[x]/(x^2 - x + 1), d = -3;
%e n = 3, F = Q[x]/(x^3 - x^2 + 1), d = -23;
%e n = 4, F = Q[x]/(x^4 - x^3 + 2x - 1), d = -275;
%e n = 5, F = Q[x]/(x^5 - x^3 - 2x^2 + 1), d = -4511;
%e n = 6, F = Q[x]/(x^6 - x^5 - 2x^4 + 3x^3 - x^2 - 2x + 1), d = -92779;
%e n = 7, F = Q[x]/(x^7 - 3x^5 - x^4 + x^3 + 3x^2 + x - 1), d = -2306599. (End)
%Y Cf. A006554, A343290.
%K nonn,hard,more
%O 2,1
%A _N. J. A. Sloane_.
%E Definition clarified by _Jianing Song_, Apr 29 2021