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.

A278790 Number of real cubic fields with discriminant <= 10^n.

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%I A278790 #22 Jan 01 2017 04:47:45
%S A278790 0,2,27,382,4804,54600,592922,6248290,64659361,661448081,6715824025
%N A278790 Number of real cubic fields with discriminant <= 10^n.
%C A278790 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 A278790 The number of real cubic fields with discriminant <= X is asymptotic to X/(12*zeta(3)) = (0.069325...)*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 A278790 Henri Cohen, Advanced Topics in Computational Number Theory, Springer, 2000, p. 426 (and Chapter 8 more generally).
%H A278790 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 A278790 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 A278790 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 A278790 Cf. A006832, A278791.
%K A278790 nonn,more
%O A278790 1,2
%A A278790 _Christopher E. Thompson_, Nov 28 2016