cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A278791 Number of complex cubic fields with discriminant >= -10^n.

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%I A278791 #16 Dec 08 2016 18:13:54
%S A278791 0,7,127,1520,17041,182417,1905514,19609185,199884780,2024660098,
%T A278791 20422230540
%N A278791 Number of complex cubic fields with discriminant >= -10^n.
%C A278791 Belabas invented an algorithm to identify all cubic fields with a discriminant bounded by X in essentially linear time, and computed the above values up to a(11).
%C A278791 The number of complex cubic fields with discriminant >= -X is asymptotic to X/(4*zeta(3)) = (0.207976...)*X. The second order term was conjectured by Roberts to be a known constant times X^{5/6}, and this was subsequently proved by Bhargava et al.
%D A278791 Henri Cohen, Advanced Topics in Computational Number Theory, Springer, 2000, p. 426 (and Chapter 8 more generally)
%H A278791 Karim Belabas, <a href="https://doi.org/10.1090/S0025-5718-97-00846-6">A fast algorithm to compute cubic fields</a>, Math. Comp. 66 (1997), 1213-1237.
%H A278791 Manjul Bhargava, Arul Shankar, Jacob Tsimerman, <a href="https://doi.org/10.1007/s00222-012-0433-0">On the Davenport-Heilbronn theorems and second order terms</a>, Invent. math. 193:2 (2013) 439-499.
%H A278791 David P. Roberts, <a href="https://doi.org/10.1090/S0025-5718-00-01291-6">Density of cubic field discriminants</a>, Math. Comp. 70 (2001), 1699-1705.
%Y A278791 Cf. A023679, A278790.
%K A278791 nonn,more
%O A278791 1,2
%A A278791 _Christopher E. Thompson_, Nov 28 2016